How to retrograde Catalina back to High Sierra

Target display mode will not work with Macs introduced after 2019 Use your iMac as a display with target display mode - Apple Support

If you don't use the iMac sell it and buy a decent stand alone display.

Since reading compression doesn't seem to be a strong suit of yours I've bolded some pertinent information for you from the link I posted.

iMac models introduced in 2011, 2012, 2013, and mid 2014

To use any of these iMac models as an external display:

• The iMac used as a display must have macOS High Sierra or earlier installed.
• The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
• The cable connecting the two Mac computers must be a Thunderbolt  or Thunderbolt 2  cable.

Good luck with your issue.

To perform this action will require booting from a Bootable Installer. 

This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer. Example : Bootable Installer of High Sierra would have to be done on a computer that Qualifies to run High Sierra

Understand this will WIPE ALL DATA and there is No Recovery - Period.

Once that is done read on for preparing the Destination computer 

>> Only works on Intel Based Apple Computers.

1 - Shutdown computer and disconnect all external drive Except the newly created Bootable Installer.

2- Restart and immediately hold the OPTION key until the Startup Manager appears and choose the USB Drive. 

3 - It will present options >> Disk Utilities >> View >> View ALL attached Drives. 

4 - Choose the Upper Most Drive ( not the volumes indented and list below ).

5 - Formatting for macOS 10.13 High Sierra and below requires HFS Journaled with the GUID Partition Map

6 - Once that is done >> backup out of Disk Utilities and choose install macOS. 

7 - Follow the prompts and it may automatically reboot several time. 

8 - Upon a final reboot - Setup Assist will present with the newer version of macOS.