If Migration Assistant does its job properly, no system-related files will transfer that cannot run on an M1 Mac. Worst case scenario, if you elect not to transfer this option, is that you will need to set up your Mac's network setting again. Typically, not a big deal.
The other thing you should be aware of is if you create a user account on the new M1 Mac with the same name as you were using on the old one, MA will try to create a second user account with that same name. So if you did so on the new Mac, you may want to consider removing it.
For an example. When I set up a new Mac, I let the installation process create the original Administer-level account. I name it anything but the name of the user account I use day-to-day on my old Mac. Once the new Mac goes through the initial setup process, I when use MA to migrate my day-to-day account to the new Mac. Since it has a different user name, than the one created by macOS, I don't run into this issue.
However, you can save yourself all of these issues, by using the Setup Assistance when you first power-up the new Mac instead of using MA afterwards.
Ref: Set up your iMac - Apple Support