mac mini and IMac 21.5 mid 2011

I believe 10.15.7 was the ultimate version.

To downgrade:

• 1: Create a new redundant backup if you value your data.
• 2: Change T2 security to allow booting from external drives with medium or lower security. https://support.apple.com/en-us/HT208198
• 3 Install Catalina from...
• -- a) An old Catalina backup.
• -- b) Internet recovery (hold shift-option-command-R) https://support.apple.com/en-us/HT204904
• -- c) A USB Catalina installer. https://support.apple.com/en-us/HT201372
• 4: Use migration assistant to restore your data from your new backup.
• 5: Upgrade to 10.15.7

Personally, I'm going to vote 'Not worth the effort. Stick with standard external monitors)', but your choice.

Hello dario1981.

Thanks for reaching out to Apple Support Communities. We understand that you need help with using Target Disk Mode for your Mac mini and iMac. We will be glad to assist.

Please see the following article for the proper steps to place your Mac into Target Disk Mode:

Transfer files between two Mac computers using target disk mode

Check out this resource for help with upgrading your Mac mini to the latest version of macOS Big Sur:

How to upgrade to macOS Big Sur

Cheers.

1. Thunderbolt 1 and Thunderbolt 2 cables are identical.
2. Yes, the 2018 mini is supported by the latest version of Big Sur.
3. Sadly Big Sur does NOT support using Target Display Mode.

I'd suggest you get a normal external monitor to use with your mac mini.