how to reconnect Beam onto Sonos system

Not sure what the ‘power off protocols’ are. Did you unplug the TV and the Beam from the wall for at least two minutes (five is probably better)?

It won’t be fixed by turning ‘off’ the TV with the remote or a button on the TV, that only sleeps the TV and Beam, and doesn’t force a restart/reload of the necessary OS.

Alternatively, you could submit a system diagnostic within 10 minutes of reproducing the issue, and call Sonos Support to discuss it. Don’t post the resulting diagnostic number here.

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.

When you speak directly to the Support staff, they have tools at their disposal that will allow them to give you advice specific to your network and Sonos system.

Oh, it might also be worthwhile, once you’ve unplugged the Beam from the wall, to reboot your router. Once the router comes back up, and after that two or five minutes, plug back in the Beam. Normally, at this point, it should show up again in your controller. 

Usually one of the two above work for recovering from power failure issues, if they don't try:

Power down all Sonos, reboot router and controller then power up your Sonos.  

Glad you didn’t find the article on how to reboot the Beam which I take it you meant perform Factory Reset. In any event NEVER factory reset a Sonos product unless instructed to do so by Sonos Tech Support.

To your case….you said you can still play TV audio via the Beam; but you can’t see it in the app. If all other Sonos are  showing in the app a simple delete and reinstall of the app on your device may have resolved the issue. Upon reinstall select “join existing system”. Did you try that?