I am having the same problem, I am currently on support chat to Apple to see if we can fix the problem.
So far we have done the following:
1. Turn off the watch (hold side button (while not on charge) and then swipe to power off like iPhone)
Then Reset the watch
1. Hold the Digital crown and the side button and the same time until you see the apple logo
Put on charger and see if it charges.
If this does not work do the following:
1. reboot iPhone
2. go to apple watch app
3. in the apple watch app got to > general > reset > erase all content and settings
4. wait for watch to erase and reboot to language screen
5. Set up the watch until you see the app bubbles
(a difference i noted at the point of first installation was, that the linking with my iPhone didn't work with the camera, i had to do it manually with bluetooth codes, not sure if this was the problem to begin with, however now with erasing and starting fresh, the linking has worked properly with the camera)
and my watch is now charging properly. You may not need to do all of these steps but its worth a try!