Limited Edition Badges in Apple Watch not showing anymore

That's pretty good if they still appear on the Watch app. I would not be that worried about it..., give it a couple more days to settle and see how things evolve.

If the issue still remains, you could also delete the Activity app and then reinstall it. That might give it the required push to sync everything back in.

Delete built-in Apple apps from the Home screen on your iOS 14 or iPadOS device or Apple Watch - Apple Support

Yes there is that kind of sync issue with the limited edition badges now and then. Have you checked if they are still displayed on the watch itself, or are they gone there too?

Which series of the watch is it? Anyways, my kind of lame recommendation for this is to close all apps, restart both devices and then just hope that the next sync with iCloud.com will bring them back. In most cases that seems to happen automatically. I am thinking that one possible reason is that the sync pull occasionally times out, and the limited edition awards are possible the last ones on the list to be pushed across.