Client ARD is not active

That client is corrupt.

Remote management is part of the operating system.

It's not an add-on.

There's no removal mechanism for remote management.

It may well be possible to troubleshoot what happened here that caused the corruption, but that's going to be more work and more thought and more than a little rummaging to get to that knowledge.

And it's not at all clear that there aren't other problems waiting within that corrupt client. Either latent problems, or problems or corruptions that might arise anew when some future macOS patch or update is applied.

I know you really want to understand the trigger. I certainly would, too. But that's a whole lot of work, and — even with that information — it may not be reasonably feasible to unsnarl whatever has happened with that client. So you may well end up performing all that troubleshooting-related work for naught.

Back up the contents of that client externally. Then reinstall macOS over macOS, if you've not tried that. If that fails, get out the Bigger Hammer, and wipe the disk, reinstall macOS, and migrate in the data.

I'd back up to external storage once or twice and reinstall and that should be harmless to the existing contents of the system, as the binoculars are part of the client settings and the screen-sharing and remote management bits are part of the macOS operating system and separate from the Apple Remote Desktop package. Failing the reinstall of macOS over itself, I'd next try wiping the disk and reinstalling macOS and migrating in the data from the backup. I'd wonder what else might be stuffed up from whatever failure or corruption arose here, too.