The new Mac is incompatible with target display mode, which by the way has finally been abandoned by Apple with the release of Big Sur.
FYI - As Apple states them, here are the rules for target display mode on iMac:
click> https://support.apple.com/en-us/HT204592
Per the link above:
• Make sure that your target iMac is using macOS High Sierra 10.13.6 or earlier.
• The source Mac must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed.
There may be an option available to you as a new feature in Monterey: AirPlay to Mac.
AirPlay To Mac – Available on MacBook Pro (2018 and later), MacBook Air (2018 and later), iMac (2019 and later), iMac Pro (2017), Mac mini (2020 and later), Mac Pro (2019), iPhone 7 and later, iPad Pro (2nd generation and later), iPad Air (3rd generation and later), iPad (6th generation and later), and iPad mini (5th generation and later). Older iPhone, iPad, and Mac models may share content at a lower resolution to supported Mac models when “Allow AirPlay for” is set to “Everyone” or “Anyone on the same network” in Sharing preferences.
Monterey new feature demo - Airplay to Mac - Mr Macintosh youtube