My iMac takes almost 5 minutes to boot up or restart after upgrading to Ventura 13.4

Try Booting the computer without any External Drives attached.

They can be reattached once fully booted

If still slow, proceed to the 7 Steps below

Suggest the User start with Points 1 to 4 and then Test

Still having issues, move onto Steps 5 and 6 and Test Again

Still no resolve - move onto Step 7 and follow instructions therein 

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Safe Mode will also eliminate Third Party Software, extensions and drivers from loading. It will only load the Minimum amount of Core Apple Processes to allow the the computer to function at a reduced Level of Performance 

3 - Does the issue present in this mode ?

4 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

5 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

6 - If the issue is present in the dummy account - then, this appears to be a System Wide issue on the computer.

7 - Download the Application Etrecheck directly from the Developer.

This is a Diagnostic Tool that makes no changes to the computer.

It makes a coherent and readable inventory of both the Hardware and Software used on the computer 

The application is free or paid from added features. 

The Report will Not Reveal Any Personal Information. 

Post back the Full Report - copy and paste - >>>> using the Additional Text Icon ( 3rd Icon to last ) <<<<

The Internal Drive reports a semi-normal size of Empty Space - to not an issue there.

But the below is directly connected to >>

Q -  System extensions installed - This computer has system extensions installed. System extensions can be difficult to uninstall.

A - There are Third Party Extensions installed that maybe interfering with the Normal Operations of both the External Drive and the General Operations of the computer 

If I may refer back to Original Reply about Safe Booting

" Safe Mode will also eliminate Third Party Software, extensions and drivers from loading.

It will only load the Minimum amount of Core Apple Processes to allow the the computer to function at a reduced Level of Performance

I do not believe there is a single issue that maybe causing this issue but a Combined Combination if issue that is resulting in this Issue

Thee reported Fact that Some Boot work normally in evidence enough to infer this is a Combination Od Third Party Software installed and used on this computer

A - Western Digital Software, Surfshark etc

A - And then the USB 2 Drive

Perhaps my learned colleague @etresoft may chip in too with additional information on this matter

Firstly, would suggest booting the computer without the 3 different External Drives and Test if the boot time is faster

Problem: Computer is too slow

Description: Boot or restart takes 5 minutes since upgrading to Mac OS Ventura 13.4

Q -  System extensions installed - This computer has system extensions installed. System extensions can be difficult to uninstall.

A - There are Third Party Extensions installed that maybe interfering with the Normal Operations of both the External Drive and the General Operations of the computer 

Q -  Apps crashing - There have been numerous app crashes.

Q -   Unsigned files - There are unsigned software files installed. These files could be old, incompatible, and cause problems. They should be reviewed.

Q -   Unsigned files - There are unsigned software files installed. These files could be old, incompatible, and cause problems. They should be reviewed.

A  - This generally indicates some of the Applications need to be reviewed for Compatibilities Issues 

Q -   System modifications - There are a large number of system modifications running in the background.

A - There are consequences when running an operation system which has been modified. This can be done by either the User and / or Third Party Application with alter the Normal Functionality of the OS

iMac (Retina 4K, 21.5-inch, 2019)

Q - Drives:

  disk0 - APPLE SSD SM0256L 251.00 GB (Solid State - TRIM: Yes) 

A - Rather small Internal SSD Drive. So, would it be correct to say a lot of your Data and Work is being kept and saved to the External Drives ?

A - If so, you may get better performances from 3 SSD Drives. The speed would be much greater that an Rotational Platter drive even if the External Drive was spinning at 7200 ROM

 Q1-  disk2 - Fantom Drives 14.00 TB

  External USB 5 Gbit/s USB

    disk2s1 - EFI (MS-DOS FAT32) [EFI] 210 MB

    disk2s2 - M************A (Journaled HFS+) 14.00 TB (5.80 TB used)

 Q 2 -  disk3 - WD Ext HDD 1021 3.00 TB

  External USB 480 Mbit/s USB

    disk3s1 - M************C (Journaled HFS+) 3.00 TB (2.85 TB used)

 Q 3 -  disk4 - WDC WD60 EDAZ-11U78B0 6.00 TB

  External USB 5 Gbit/s USB

    disk4s1 - EFI (MS-DOS FAT32) [EFI] 210 MB

    disk4s2 - M************B (Journaled HFS+) 5.00 TB (1.17 TB used)

    disk4s3 [APFS Container] 1.00 TB

      disk5 [APFS Virtual drive] 1.00 TB (Shared by 1 volumes)

        disk5s2 - M************D (APFS) (176.21 GB used)

Q -   Surfshark.app

 Q -   [Running] Surfshark Antivirus - version 4.9.2 (SURFSHARK LTD - 2023-05-22)

    Application: /Applications/Surfshark.app - version 4.9.2 (SURFSHARK LTD - 2023-05-28)

    Description: System Extension enables Surfshark app to provide antivirus features.

Q -  [Running] Surfshark. WireGuard - version 4.9.2 (SURFSHARK LTD - 2023-05-22)

    Application: /Applications/Surfshark.app - version 4.9.0 (SURFSHARK LTD - 2023-05-28)

    Description: System Extension enables Surfshark app to connect using WireGuard protocol.

A - VPNs are usually good or required for Connecting to the HeadOffice Network and or Banking websites. If the intent is to protect your Internet Connects - waste of time IMHO.

A - Many VPNs collect your personal Data and Credit Card Information and repackage it for Sale,

A - After all, VPNs are  in business to make Money 

Q -  qbittorrent.app

A - Torrents are a  Great Way to download Pirated, Cracked and often times  Malware / Adware infect software without the user even being away of this fact.

Q -  Launchd: /Library/LaunchDaemons/com.wdc.WDPrivilegedHelper.plist

    Executable: /Library/PrivilegedHelperTools/com.wdc.WDPrivilegedHelper

    Details: Exact match found in the legitimate list - probably OK

A - Third Party Software from the Manufacture that is bundled on the New Drive is very often Buggy. Added is the fact that macOS is very well equipped to manage external drives

I would do 2 things:

Run 'First Aid' from the disk utility app

Boot into safe mode to allow the system to run diagnostics and repair what it finds wrong.

Start up your Mac in safe mode - Apple Support

Then boot back into regular mode and check if problem has been resolved.

Try booting without that USB 2.0 drive connected and see if there is a difference.

Welcome

" I hardly ever use the VPN. I'm thinking compatibility could be an issue."

Although is is hardly used makes not different is use often or Not.

It is installed and Running in the background ALL the Time

Thank you 👍 for the Report. 

We and that is a Collective We, meaning other contributors and self, will dissect it in detail. 

Will get back to you shortly

Good catch USB 2 drive and " early bird gets the worm ? " 😎