I looked to see if this had been reported yet. Running the first developer build of MacOS Monterey and Tailscale no longer functions correctly. The program opens and appears to function as if you were not logged in. When attempting to login, the program just does not respond with any output. Does not bring up Login screen or provide an error.
Please subscribe to macOS 12 (beta): tailscaled socket doesn't come up · Issue #2074 · tailscale/tailscale · GitHub for updates.