Disable auto start for array, docker and VM's (if you have any). Be sure to have a clean shutdown.
For good measure make a copy of config folder, found on your unRAID USB. This way if something happens you have a backup already prepared.
Swap over to the new, then start. I've done this a few times over the 10+ years with unRAID, it's a treat it works this way.
If you want to be a little more sure you could:
Verify the new motherboard can boot ok from USB before you migrate over. Maybe start with an Ubuntu, or other distro, live USB. Then you can use a trial version of unRAID to verify that boots. This could save you before you transfer everything over. Also from trial unRAID can verify if your network card/onboard works too.