This sounds like a monitor setting issue. If we look at EveryMac M2 specs
[quote|format=featured]This model supports "up to two displays" -- one "up to" 6016x3384 (6K) resolution at 60 Hz over Thunderbolt ''and'' one display with "up to" 5120x2880 (5K) resolution at 60 Hz over Thunderbolt ''or'' 3840x2160 (4K) resolution at 60 Hz over HDMI.[/quote]
So here’s the possible display support. Review the displays or TV’s frequency support as it’s likely the display can’t support the higher resolution the Mac Mini is trying to drive it. The reason it starts off working and as soon as you select the drive the OS’s setting take over.
* 3840x2160 (4K)
* 5120x2880 (5K)
* 6016x3384 (6K)