I have had the same problem with my Series 5 ever since Watch OS 6.0.1 After every WatchOS update the watch gets stuck at 100% battery until it shuts off due to no battery power. After the shutoff, it has behaved and shown a battery strength that moves up and down as I use and charge the watch.
The update to WatchOS 6.1.2 has been no different.
However, I think I do have some good news. After reading the later posts in this thread I powered my Series 5 ( which was showing 100%) off for about 15 minutes. When I powered it back on, it showed 95% and then dropped within 10 minutes to 53%.
I think a power off for 15 minutes after every WatchOS update might be the solution until the WatchOS bug is fixed.