My wife recently bought a mighty mouse. It worked for a few days, but then macOS would fail to associate with it via Bluetooth unless it's plugged in via the lightning cable, in which case it's unusable, the connector being on the side that normally sits on the table.
Anyways, after a quick Google, I found a workaround that I couldn't believe would work, but I tried it anyways: open preferences, and check off "Allow Handoff between this Mac and your iCloud devices". ... and it worked instantly.
My wife doesn't even have an iCloud account...
The problem (and workaround) has been known for at least 4 years.