Magic Mouse 2 "connection rejected"

I know this has been asked before but those conversations were resolved and closed. My magic mouse recently stopped connecting. It says "Connection rejected" every time I try to connect it. Other bluetooth devices are working fine.

Things I’ve tried:

• Updated Mac OS (running Monterey 12.5)
• Removed and re-added the mouse in the Bluetooth preference pane.
• Connected the mouse via the charging cable - it says it’s connected and charging, and I get a pop-up notification that the mouse is wirelessly connected. But then it disconnects when unplugged, and switches to “Connection rejected” again.
• Deleted Bluetooth preference files.
• Reset the Bluetooth module in Terminal.
• Restarted in Safe Mode, and the problem persists there.
• Connected it to another computer. Same thing: it recognizes it when it's connected via the lightning cable, but will not connect otherwise.

At this point, I'm wondering if the mouse is just broken?