Non-Apple mouse won't stay connected?

It could be static electricity. Years ago as a tech I had an entire lab of computers with mice and keyboards randomly cutting out with a second lab with the same equipment had no such problems. The sole difference between the two was the problem lab had carpet and the other was tiled. I wound up giving the instructor a spray bottle of diluted fabric softener to spray on the carpet each morning during the winter.

Have you tried other ports including USB-A with a suitable C-A adapter?

👌👍

Same thing happens to me with my USB-A keyboard. I need to replug it every time my Mac boots so I can use it.

Hmm, here the Logitech (not wifi) wireless mouse works fine with the MacMini. Cheap and cheerful no doubt, but the magic mouse has a bit of a bad press and seems a little expensive for what you get.