OK, cool. I'd seen posts where the Migration Assistant on the Apple Silicon machine turned wifi back on after the user had switched it off, but I guess if it hasn't been set up in the first place, it shouldn't be an issue.
It sounds like you want to do a direct Ethernet-to-Ethernet connection to do the transfer, correct? If so, you'll need to connect the new Mac to Wi-Fi in order to activate it. To get around this, you could probably turn on Sharing from your old Mac and share your Wi-Fi internet over Ethernet. (Theoretically, that should work, but I’m not 100% sure since I haven't done that before.)
You can use Internet Sharing settings to share the internet connection on your Mac with other devices on your local network.
support.apple.com
Or are you plugging both Macs into a router that has an internet connection? In that case, you can ignore the above and can skip Wi-Fi during setup.
Just speculating here...but I’m guessing when the network stuff gets migrated over, the new Mac sees that and then connects to Wi-Fi, and/or it's syncing from iCloud Keychain once you sign into iCloud and then connects that way.
So, to be safe, perhaps forget the Wi-Fi network from your old Mac and make sure it's no longer in iCloud Keychain when it's time to do the transfer. Or to be even extra safe, turn the Wi-Fi off on the router. Of course, this might be tricky if you're doing a direct Ethernet-to-Ethernet transfer and need Wi-Fi internet for something else.
What macOS version on the 2014 Mini? If it is more than a major version or two behind the MBP, I would avoid Migration Assistant and setup the MBP manually. The automatic upgrades that need to be done to much of the content of ~/Library can be troublesome.
Agreed... AND you are going from Intel to Apple Silicon. You could potentially be copying over Intel-specific stuff that's no longer needed, or Intel-based apps when there's an Apple Silicon or Universal app you should be using instead. You could always set up the new Mac as new and still copy over your data manually through an Ethernet-to-Ethernet connection.
On your Mac, use an Ethernet cable to connect two computers and share files or play network games.
support.apple.com