I found an alternative method that worked perfectly:
https://www.youtube.com/watch?v=3U1P8e0rRyw
Exact same problem (which actually sux as my Apple TV 4K is in the basement, and my office (MacOS) is on the 3rd floor and I've had to run up and down the stairs 3 times before the pairing failed.
Would love to see an answer to this one.
One slight difference, my AppleTV is currently on 14.7
Looking forward to an answer to this as well. There are some interesting elements to the situation I'm in.As a baseline, I am on:iOS Beta 13 . 6WatchOS 6.(17R5491t).. I think that is 6.2The watch would not update after this and I submitted a feedback to see if there was a problem.I subsequently found that the beta profile for the watch had disappeared (found out after the upgrade to iOS 13.6)Eventually, I proceeded with the upgrade to iOS 13.6 and am in the same sitch you are.However, the watch is not completely dead. It can:Secure weather info if the iPhone and Watch are on the same networkPerform Watch based Apple PaySend and receive txt messages (if on the same network as iPhone).It also appears as Blootooth connected on my iPhoneUnfortunatly, the iPhone cannot connect with the watch when I initiate "Software Update" from the iPhone. Instead I get the error:Could Not Connect To Apple Watch, (make sure your watch is nearby, powered on and not in airplane mode).At this point, it appears my only option is to wait for iOS 13 Production to be released as I cannot find another way to get the Beta profile onto the watch.
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Me/3!! Already opened a feedback entry, was hoping to find support here.