My phone keeps stating that installation is paused, although my watch is on the charger, fully charged and next to the phone, fully charged.

hi, i had this problem since i bought the apple watch 7

i just switched off the watch and restart it and the problem solved!

Try to 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.