Wear App Manager runs on your phone but manages the apps you have installed on your Wear OS watch. See all your Wear apps (and only your Wear apps) at a glance, and see more details about any of them. Easily uninstall ones you're not using. Wear App Manager puts you in control of your Wear apps at last.

NOTE: Google Play frequently seems to take a while to sync ownership to the watch, during which time it won't let you install, asking you to pay again. You just need to give it a little time, and then you can go ahead. I've opened a support ticket with them, but the wheels of Google grind slowly. Leaving a 1⭐ review here helps nobody!

ALSO: it's not possible to uninstall system apps from the watch, by any means (including this app).
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WAM was the first app manager for Wear and is still the best! But don't just take our word for it:

"Some of the apps on your phone have Wear modules, but which ones? And what the heck do they do? Wear App Manager lists them all in one handy place." - Android Police

"Wear App Manager takes the guesswork out of the equation" - re/code

"It’s boring having to scroll through hundred of other apps from the settings menu. Enter Wear App Manager, a slick and easy way to see what’s taking up what on your wearable" - Android Headlines

"It’s a potentially useful tool and even more so if you’re a new Android Wear owner." - Android Authority

Full feature list:
▶ Quickly uninstall apps from watch (Wear 2 only)
▶ Notifications (on your watch, handheld, or both) when Wear apps are installed, updated, or uninstalled
▶ See permissions each app is actually using on your watch
▶ Storage space available on-device, and how much each app is using - in more detail than that shown by the Wear OS app
▶ Directly open system settings for an app, or its listing on Google Play, without cumbersome navigation on the watch (Wear 2 only)
▶ Share app details or lists with friends
▶ Launch apps (on watch or handheld) easily
▶ Shows apps installed only on watch (in development, or sideloaded), and those whose watch components are missing
▶ Sort app list by name, size, update or install date
▶ Full support for multiple wearable devices linked to your phone
▶ Lots of geeky internal details about each app, like version codes and install dates. Handy for devs!