Bluetooth issues in Ventura: Magic mouse and keyboard not working on startup

Every time I start my M1 iMac running Ventura 13.2.1, neither the Magic Mouse nor keyboard respond on the login screen. I have to plug in a spare mouse and connect the keyboard via USB in order to log in. Once I’m in, both devices work wirelessly. It’s very annoying and impractical.

I’ve tried:

• Turning the devices on and off
• Unpairing and forgetting the devices and adding them again
• Turning Bluetooth on and off
• Restarting the Mac
• Reinstalling the OS
• Resetting the Bluetooth module using pkill bluetoothd in Terminal

Anyone else with this problem and any other solutions?