How do I clear apps off of my watch so I can install the recent software update?

If you go to the Watch app on your phone and scroll down, you can see all the apps installed on your phone. Tap any app and deselect "Show App on Apple Watch" and it'll remove the app from your watch.

Try this;

Unpair your Apple Watch via the Watch app on your iPhone.

Then Re-pair your Apple Watch again,this usually frees up

enough storage space to update your watch.And without any loss of data.