Same with my Galaxy Watch 46 and Samsung Note 8. Contacted Samsung Support, sent them the phone's log files. The reply is that I can return the watch for a replacement. How inadequate these people must be to offer to replace hardware for a software issue that will be present even on the new hardware!
Just FYI - factory resetting the watch doesn't change anything. As far as I can see, there is no way to update the app from the watch directly - in the My Apps list it shows all apps I have installed manually, but not the factory preinstalled ones.
The cache cleaning on the phone apps and services didn't work either.
This is a widespread problem reported all over the world. The ball is in Samsung to quickly provide a solution. Keep sending Samsung Support reports, so that they can sooner acknowledge the scale of the problem.
Hey guys I've got a some good news for you. At least
most some of you I've just updated Samsung Health on my Galaxy Watch 42mm.
There are two ways of doing this. The fist one works for some users only - but not me, so I've had to use the second one. Here we go:
1 - Turn OFF - BT on the Watch
2 - Enable WIFI and connect to some Wireless Network
3 - Hit Home button (Lower) and Launch Galaxy Store
4 - Tap three dots on the right side -> My apps -> AND SEARCH FOR -> Samsung Health -> Tap IT.
--- If you can see an option to UPDATE the app -> Option - 1)
5 - DO IT, and wait until it finish updating itself.
6 - Once completed, turn on BT and continue using it as usually.
--- If you CAN'T see an option to UPDATE the app, just an option to Run it -> Option - 2)
5 - you need to go back to the options and RESET your watch - I had to do that for some reason.
6 - pair it again, don't launch Samsung Health on the phone. Jump back to the point  - should work.
Anyways. I still can't see an option to select Galaxy Watch (as a source for my step counter - just ALL or my mobile) in Samsung Health on my phone. That's still an issue. Let me know if that works for you. Fingers crossed.