Hi Daniel,
The macOS versions shouldn't need to match for Migration Assistant. I could be incorrect about that, but regardless even if you try to migrate, you won't hurt the data stored on your 2012 MacBook Pro.
If you have the correct cables (Thunderbolt 2 cable + Thunderbolt 2 to Thunderbolt 3 adapter), you could also put your 2012 MacBook Pro into Target Disk Mode (hold down the T key at startup, hold down the power button to shut down when you're finished) and connect it to your M1 MacBook Air. With Migration Assistant open on the M1 MacBook Air, that should be guaranteed to work.
Unfortunately it's outright impossible to run macOS Catalina or earlier on an Apple silicon Mac, such as your M1 MacBook Air. Not only does it violate the rule that you can't downgrade from the shipping macOS version, but macOS Catalina and earlier only support Intel processors (not the M1 chip).