Magic Mouse not detected since Ventura

I have encountered a similar problem after upgrading my Intel-based 2017 iMac to macOS Ventura. If I need to boot or restart my system, I need to use an older Magic Mouse with USB connector until I can log into my emergency "root" account on Macintosh HD, open System Settings>Bluetooth, and connect the Magic Mouse 2.

After doing this, I can log out of my emergency "root" account and log into my normal user account that is on an external SSD drive.

I'm beginning to believe my son-in-law (an Apple employee) has the right approach. Don't upgrade until after the first upgrade to a macOS release is available.

My Magic Mouse 2 isn't recognized until I log into my emergency "root" account and Bluetooth is enabled. There is no need to plug it in.

All my configuration information for my "normal" login is on an external disk. It was configured that way when I needed to move to a 4 TB disk mounted in one of the disk trays in my 2008 Mac Pro. When the Mac Pro had a fatal hardware failure in 2017, I was able to move the disk to an external chassis attached to a 2017 iMac that I had purchased as a replacement for the Mac Pro.

No problems until Ventura started complaining about a fatal login problem.

As a Magic Mouse is cordless, how do you plug it in with a cable?