"Installation paused" Apple Watch update error

Well I quess you have it on the charger and connected to the same Wifi? How about if you try to install the update from the watch directly - what happens then?

Update from the watch itself.

Place the watch on the charger.

Make sure that your watch is connected to wifi.

On your watch, open the Settings app.

Tap General > Software Update.

Tap Install if a software update is available, then follow the onscreen instructions.