Hi there!
I found a solution to your (and my) problem, in case you haven't found one yet.
1. Delete the already downloaded watchOS update in the Watch app (if you haven't done so already).
2. Force restart your iPhone (hold power- and home-button until the Apple logo appears).
3. Force restart your Watch (hold side button and crown until Apple logo appears).
Now, after both devices are powered back up, you should be able to install the app-updates from the Watch app on your phone. Strangely, already updated iPhone apps with Watch apps were not pending automatically for installation - I had to manually start the update/reinstall process.
Hope this helps!
Best regards,
VSG