Apple Watch Series 4 doesn't appear in Apple TV 4K list of devices

Yes I can access music and photos for example and scroll through these and get them to play as well as the menus in the Apple TV main screen and Settings. Its not the smoothest process though and slow in reaction. On the Watch screen bottom left I have a Menu button, bottom right play/pause button, top left blue lines which return me to a Remote menu list and top right has the digital time.

I can also see when I am playing media a very blurred image of the photo or song album cover in the centre of the screen.

Just thought I can send you a screen shot. Hope this helps.

Thanks for your response and sorry I should have been more specific.

On the Apple TV its Settings/Remotes and Devices/Remote App and Devices, then the paired Devices list appears.

Under the instructions I have read to pair the Apple Watch the name should appear in the list of devices which I should then click on and get a code which then confirms the pairing. I have my Mac, iPhone and iPad showing on that list. I don't recall ever pairing the watch but I must have done as it can control the Apple TV.

I have removed the Apple TV from the Watch and then gone through the process again and it pairs again but again without appearing on the list.

Wild guess - because the phone is showing on there is that effectively also the pairing for the Watch?

Yes I think that can be the only answer, just a bit odd that Apple mention specifically that the Watch will appear in the devices list, but hey ho there will always be the odd glitch somewhere, at least it works. I very much appreciate your time and thoughts on the matter, thank you.

Yes that is correct. Thank you.