See this requirements for target display mode
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.
As you can see, your new MBP is not compatible with target display mode. As a first, it has difficulties to work on a laptop with any OS higher then Catalina.
As a second, you will need to use a thunderbolt 2 cable and your new MBP does not have thunderbolt 2 ports. Target display mode will not work with dongles
Use your iMac as a display with target display mode - Apple Support