Trying to transfer data from an old Mac Mini to a new one using Migration Assistant.

This should help;

https://support.apple.com/en-us/HT204350

Large migrations over Wi-Fi, are prone to fail and using direct Ethernet connection is only a little better.

The fastest, best and most reliable way to do large migrations, is to connect your old Mac's Time Machine backup or bootable clone backup to the new Mac and migrate form it.

in addition to the comments above, you should use a wired USB connection. The transfer should easily be accomplished in an hour or so. Be sure to follow the directions. First, set up the new computer, then when prompted, connect the two computers and activate Migration Assistant. It should go without any problems.

Wi-Fi is very slow. I'd never use Wi-Fi with Migration Assistant. As suggested above, there are much better ways to use Migration Assistant.