back OS versions

It depends on the operating system and if you have a Time Machine backup of the previous operating system still available. If true, then you can boot into Recovery, and select Restore from Time Machine Backup.

Otherwise, and unless you have a clone of the previous operating system on an external drive, I would advise not reverting the operating system as it would require formatting (wiping) the drive, and performing a clean installation of the desired operating system, without a means to migrate your previous personal data and settings.

It might be better to state the problem that is influencing your decision to revert the operating system and see if we can find a remedy allowing you to stay on the current operating system.

I don't recommend any. 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 user tip describes what you need to know and do in order to protect your Mac: Effective defenses against malware and other threats - Apple Community   

All of my Big Sur installations took at least 30 minutes. With Big Sur there are not update files available from Apple's Downloads site. It's all thru the System/Softrwre Update or App Store.

What exactly were the problems you were having with Big Sur?

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

What Mac model do you have? How much RAM? Size and type of boot drive and how much free space?

This is very strange. My wife has the same machine only in the 27" model and we're experiencing no significant sluggishness.

As a troubleshooting tool, take a look at Activity Monitor in /Applications/Utilities and see if there are any apps hogging a bunch of CPU cycles:

If not, also look at the "Disk" and "Network" panels to see if anything is using an inordinate amount of resources. Finally check your CPU load panel. With nothing going on you should be at 10-20% tops.

As I'm typing this, I am starting to wonder if you've picked up some malware and somebody is doing Bitcoin mining on your machine, which has been known to cause significant sluggishness (because it's so CPU-intensive). You can download a free trial of several malware detection packages ... I use MacScan but your mileage may vary. That would be one way to see if something nefarious is going on.

While it is technically feasible to downgrade to an older OS from a newer one, it is a perilous path fraught with challenges. If you don't have a Time Machine or other backup dating to when you were using Catalina OS, you may find that many Catalina-era apps are unable to read the Big Sur-era databases, including Photos, Mail, and Contacts. Rather than go into details here, I recommend you study this third-party web page:

https://bombich.com/kb/ccc5/best-practices-updating-your-macs-os#commit

In particular, read the section entitled "If you have to downgrade, here's what you need to do". Then you can decide if you want to do the downgrade.

I have not read in any of your thread follow-ups that you have a Time Machine backup of Catalina, or that you had, but used the same drive for Big Sur backups?

As this is a 2017 iMac purchased in 2020, I am wondering out loud about the health of your Fusion drive, and if it might be in some stage of failure or corruption. I suggest booting the iMac into Recovery (⌘+R) and run Disk Utility First Aid on the entire drive. You should receive a green ok, and if not, run Disk Utility First Aid again. Then reboot normally.

If you are opening too many concurrent applications or leaving them open with your minimal 8GB of RAM, then this will cause a significant slow down as you could be exhausting available RAM, and the operating system is forced to use slower, rotational storage as a RAM substitute (known as swapping).

The full Catalina 10.15.7 installer is 4.9 GB. The full installer for Big Sur 11.2.3 is 12.6 GB. That is a 157% increase over Catalina and will place greater demand on your RAM and slow mechanical storage.

robertbk wrote:

The only back up I've performed then, was when syncing my iPhone.

If you don't have a backup strategy, i.e. like Time Machine or cloning your boot drive to an external hard drive, it's like driving without a seatbelt - you don't need it until you do.

If the computer Came with Big Sur pre-installed - the answer is No it can not be done. Otherwise - the instructions and directs of @Peter Jones4 are a good direction.

Not so with the security updates. But all of the system updates did.