One thing you can try is that:For the Polar smartwatch the watch does apear in the bluetooth settings, but not in the WearOS app.
It must be connected via the app first, or it would not be paired properly.
For the LG TV, it does not apear in the screen casting settings at all.
Edit: It may be an issue with the quoting in this website at the moment, as I did try to quote anwaya Paul here, but it did not apear in my reply.
1. Restarting the phone
2. Connecting the watch normally from blootooth menu ( not from wear os app), and after connecting click on forget device. And then try to connect it from wear os app.