My Apple Watch is no longer paired to my iPhone

For some reason, my wife's Apple Watch no longer shows on her phone's Watch app (the app shows no devices paired). We can see the watch in the Find My app, but not in the Watch app.

Somebody suggested making sure the watch has the latest software update, and the watch will let me click Install (through the Settings > General > Software Update menu), but then we get a message, "To install the Apple Watch update, view and accept the terms on your iPhone," which of course we can't do.

I've tried to do the Start Pairing step in the Watch app, but it never finds the watch (as the watch probably isn't discoverable, because I assume the watch thinks it's already paired).

Is there a way to force the watch to be discoverable, or have the Watch app on the phone re-connect somehow, or is our only option at this point to erase the watch using the Find My app and then start over? (Our issue with that last option is that then we lose everything on the watch since it can't be backed up first.)

[Re-Titled by Moderator]