same issue with MBP M1. It asks for the computer password 2 times to install (usually it is only once) and then it fails. Multiple reboots and still the same issue.

Issue is resolved and the app is working on the watch. Restarted iPhone and Watch - app still did not work. Waited around 1/2 an hour and tried it again and now it works. No other settings were changed - just a bit of a lag in enabling the app on the watch - weird.