Missing Reminder Lists on Apple Watch after iOS13 and watchOS 6.0 upgrade

I just found the solution to this. Open Apple Watch app on your iPhone, then select General / Reset / Erase App Watch Content and Settings. This only takes a couple of minutes, then you will be asked to add another Apple Watch (just re-add the same Watch). I used the RESTORE FROM BACKUP option. Once restored, it may take a few more minutes for you reminder lists to synchronise, so your lists won't all be visible during that time. It took roughly 4 minutes for my lists to appear on the Apple Watch Reminders app.

If you have an iPad, then maybe check you your are running the new iPadOS. That will update reminders on your iPad to the new format (in case that is causing sync problems across other devices). You could also check your reminders lists at www.icloud.com to see if all your lists are visible there. If they are not, then you have a different problem.

One more thing I tried which I did not mention; while I was waiting for the reminders lists to update on my Apple Watch, I added a new list on my iPhone (I just called it "test"), checked that it appeared online, then deleted it again. It may have triggered the Apple Watch to update all the lists, but that's just a guess.

The nuclear option would be to restore your Apple Watch as a NEW APPLE WATCH, instead of RESTORE FROM BACKUP. I did not use this option because I didn't know what information I might lose in the process. Try this as a LAST resort.