Updating Mac to 12.6 (21G115) didn't help - still won't talk to iOS 15.7 (19H12). I will try the workaround.

The Xcode 13.4.1.xip worked for me. Download here: https://xcodereleases.com/ Unzip it, launch it, connect the device. After it initialized the device, I was able to deploy to the iPad.