big sur or catalina?

You are or your friend is right, that, it is indeed an option : resetting mac computer to factory-settings can also speed up a mac computer,

BUT fine-line texts are : it may not give that mac computer the latest macOS if that mac computer is not compatible with latest macOS , in such case : you will get an older macOS version that was supplied with it when it was 1st time released from apple factory. But you can then manually upgrade it again to a higher macOS version what is possible safely.

WARNING : IF "RESET" IS DONE , THEN ALL EARLIER DATA, CONFIGURATIONS, INFO, ETC WHICH ARE DOWNLOADED OR STORED IN APPLE MAC COMPUTER , ALL SUCH DATA WILL BE ERASED FROM APPLE MAC COMPUTER'S STORAGE DEVICES/DRIVES.

SO IF THERE IS NO PROPER BACKUP DONE (IN "TIME MACHINE" OR IN "ICLOUD" etc) THEN YOU WILL NOT GET BACK YOUR EARLIER DATA.

More info on STARTUP KEY/BUTTON combinations:

Mac startup key combinations - Apple Support

How to reinstall macOS:

How to reinstall macOS - Apple Support

How erase a mac (Apple ARM / Apple Silicon / M1/M2 etc):

Use Disk Utility to erase a Mac with Apple silicon - Apple Support

How erase a mac (Intel-basd):

Use Disk Utility to erase an Intel-based Mac - Apple Support

macOS Recovery/Reinstall/etc on AppleSilicon/AppleARM/M1/M2/etc:

Use macOS Recovery on a Mac with Apple silicon - Apple Support

More info on Factory Reset of macbook computer (for Monterey, Ventura & later macOS):

Erase your Mac and reset it to factory settings - Apple Support

Another option:

Restart your  mac computer (or Shutdown from macOS & then use ⏻ power button to start it) , then quickly hold down these keys/buttons in ⌨ keyboard : Command+Option+R ( ⌘⌥R ) aka WindowsFlag+Alt+R ( ⊞⌥R ) keys/buttons . This will boot into "macOS Recovery over the Internet" by using apple servers ( if necessary tools, Internet connections, etc are already present & connected ) , So in this section : you have option to erase your mac computer's Macintosh HD from the mac OS Utilities menu, and you have option to reinstall macOS . You'll get the most current version of macOS for your/this mac computer , if current version of macOS is compatible with your/this mac computer , or else : the macOS which was used during 1st time release from apple factory, that will be installed, then you can manually upgrade old macOS into a higher macOS version.

When your friend gave the computer to you, did they perform the actions as per Link below ?

If not and you intend to keep the computer, you can perform this action yourself.

This would remove the System Modification the pervious Owner had performed on the computer.

You may even find the computer will run Ventura much better that it is now

link below

What to do before you sell, give away, or trade in your Mac - Apple Support (CA)

this is your mac computer's technical specifications.

unfortunately RAM & storage-memory-SSD are soldered on mobo, (so cannot be upgraded normally by normal user).

Big Sur, is 1 major version earlier of Monterey, is+was test bed & bit still buggy, allows only 64bit apps.

Catalina, 1 major version older than BigSur, was very stable. From this macOS & newer macOS, only 64bit apps can work in macOS.

Mojave, 1 minor version older than Catalina, was okay, it allows 32bit+64bit apps.

.. and i want to clarify , there are different type of Intel processor based mac mobo (with different combinations of hardware) , there are different type of ARM/M1/M2 processor based mac mobo (with different combinations of hardware) , so ...

... different macOS ran in it with different performance level ...

if you ask ppl, which was best or better , it/opinion varies ...

if you look into macOS related responses, issues etc inside different macOS category here in apple-Discussions, ... you will notice ... it/opinion varies ...

same app, when runs in different hardware (and under different macOS), ... have different performance level, have different issues, etc, etc.

mac computer that has more RAM, those runs better, ... those with less RAM has various issues ..

mac computer that has SSD based storage, runs faster, but if storage size is limited, then hardware usefulness diminishes quickly, etc, etc ..

anyway, i suggest to use Catalina, in that mac computer, ...

... if you will not need to run 32bit macOS apps.

And FINE-TUNE / OPTIMIZE the OS for your usage & need :

it means , disable , not-delete , various unnecessary macOS services, daemons, agents, processes, etc that are just not needed by your usage case, all at same time,

it means : disable macOS services which are not used now , run them only when you need them, but those should not run in background all the time.

For-example: Siri, Spotlight, etc runs lots of search & data gathering/indexing ops inside mac computer, etc , so i suggest to disable these services.

Various graphics features which makes various things looks/appearing nice, ... those use lots of graphics computing, ... disable them.

Get LaunchControl or Lingon or other similar app, (sadly .. these are not free anymore).

( take note or take screenshot of default settings, before you make any changes : ⌘⇧4️⃣ )

Try CleanMyMac, etc, type of macOS optimization app.

Download & run EtreCheck, it is a good & free system report type of app, to know more about whats running inside at this moment, etc.

Those who want to increase security & privacy:

https://github.com/drduh/macOS-Security-and-Privacy-Guide

enable default firewall in macOS, enable stealth mode, disable incoming traffic to all services.

allow incoming only to what you want & 100% sure.

Best is to get a paid wrapper app software ( Murus, etc ) to configure macOS's builtin full PF firewall, then you can control network traffic much much better , but its still nowhere as close or as advanced as Windows Firewall or Comodo Firewall.

Firewall can stop most of the unwanted network traffic : inbound & outbound.

essential element for safety & security.

Disable gamed service, etc, if you will not play games in it:

https://apple.stackexchange.com/questions/108902/

fine-tune & optimization should make macbook computer heating-up, much less than before.

by the way, Monterey is less buggy than Ventura, exactly at this point of time (December, 2022) ... you can also fine-tune monterey too, to make it run better in your current mac computer.

macOS Catalina (last stable version) on  AppStore : https://apps.apple.com/us/app/macos-catalina/id1466841314?Mt=12

or try to download any other macOS from here : How to download macOS - Apple Support

In "Terminal", you may try:"

$ softwareupdate --fetch-full-installer --full-installer-version 10.15.7

( the 10.15.7 is the last Catalina, at this moment . Inside the appstore page you can find the last installer's version number, for any macOS mentioned in above Apple-Support webpage, then that version number can be used in (above) command-line . This download comes from apple's own servers. )

DO NOT DOWNLOAD macOS installer .APP or .DMG file(s), from any type of 3rd-party (aka: non-apple) website.

After getting the macOS-name-installer.APP file,

a user can right-click on it inside macOS "Finder",

& then user can select "Show Package Contents" option,

to go inside the APP bundle file, to browse further,

then user can find & extract the "InstallESD.DMG" file,

& that file can be turned into a bootable media/disk ( USB based or DVD-disc-based ),

so 1st convert the extracted "InstallESD.DMG" file into an ISO file :

$ hdiutil makehybrid -iso -joliet -o Catalina-installer.ISO InstallESD.DMG

( if you are making bootable for other macOS, then change the word "Catalina" in above command )

If you followed above steps, then below steps inside the below webpage, is not necessary:

Create a bootable installer for macOS - Apple Support

Then, you may use your own choice of Bootable Media/Disc creation software to create bootable media,

i suggest to use "Balena Etcher" at this moment, ( i wish it's devs were not-using "Electron" stuff ) :

https://www.balena.io/etcher/#

If the ISO file is smaller than 3.8 GB, then a USB storage drive 4 GB wud be enough.

If ISO file is larger than 3.8 GB, then a USB storage drive 8 GB wud be enough, if the iso file is not larger than 7.6 GB.

When you turn on mac computer with ⏻ POWER button, then immediately pressing the "T" button/key in keyboard means, You want to boot from another media or disc-drive.

Do this process,

and then either select USB storage or select DVD disc if you placed bootable DISC in DVD drive.

You've install what most of the experienced contributors to these forums consider akin to malware: CleanMyMac.

First, there is no reason to ever install or run any 3rd party "cleaning", "optimizing", "speed-up", anti-virus, VPN or security apps on your Mac.  This documents describe what you need to know and do in order to protect your Mac: Effective defenses against malware and other threats - Apple Community and Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support.  

There are no known viruses, i.e. self propagating, for Macs.  There are, however, adware and malware which require the user to install although unwittingly most of the time thru sneaky links, etc.   

Anti Virus developers try to group all types as viruses into their ad campaigns of fear.  They do a poor job of the detecting and isolating the adware and malware.  Since there are no viruses these apps use up a lot of system resources searching for what is non-existent and adversely affect system and app performance.

There is one app, Malwarebytes, which was developed by a long time contributor to these forums and a highly respected member of the computer security community, that is designed solely to seek out adware and known malware and remove it.  The free version is more than adequate for most users.  

So before you upgrade to Ventura uninstall CMM according to the developer's instructions. You can check to see if you've removed all of the supporting files by downloading and running the shareware app Find Any File to search for any files with the application's or the developer's name in the file name.  For CMM software you'd do the following search(es): 

1 - Name contains cleanmymac

Any files that are found can be dragged from the search results window to the Desktop or Trash bin in the Dock for deletion.

FAF can search areas that Spotlight can't like invisible folders, system folders and packages.  

I would not upgrade with CMM still installed.

Do not use/copy the 1st symbol "$" , displayed before a shell command / command-line.

copy-paste command from here, to use/paste inside the Terminal app , ( Terminal app is a shell manager app ).

By the way, some users new to using "commands" or "shell(s)" get confused with the 1st symbol "$" , & uses/pastes it in Terminal app:

please kindly read this.

thanks in advance.

You should be able to run Ventura without issue.

If it doesn't, it likely has third-party system modifications installed which are interfering with its normal operation.

It shipped with Catalina, so technically, that was the OS designed for that Mac.

Also , Be Aware : various version of macOS installer file's size can vary from 2.5 GB to 6 GB, but usually over 4GB.

So for-example, if your ISP (internet service provider) gives you 200 Mbps (Mega Bits Per Second) bandwidth aka speed , ( it means approximately 20 Mega Bytes Per Second ) , & usually this is max download speed) , then a 4GB file will take approximately 205 seconds ( that means: 3 minutes 41 seconds, if apple server can send at full speed , at what your connection can download , & Such can happen when apple servers are not overloaded / busy ).

I see no reason why Ventura shouldn't work just fine on your 2020 iMac. I've been running it on my 2017 iMac ever since the first Beta versions was released. I find it to be very fast and stable.

Do no install and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac? If you have any then uninstall them before trying to upgrade to Ventura.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Good.

There are times when In Person assistance is better.

Enjoy