Apple Watch Series 3 "Cannot Install Update" due to available storage
The alert on my watch links to this Apple knowledge base article:

If you don’t have enough space to update your Apple Watch
https://support.apple.com/kb/HT211283

At the top, there is a note specifically for the Series 3:

If you have Apple Watch Series 3, skip directly to the steps to unpair and update your Apple Watch.

This indicates that the only way to update the Apple Watch Series 3 is to perform an unpair and update.
Skip directly to that step, and don't bother manually deleting photos, music, or data.
After updating watchOS, you can unpair the watch again and restore from your previous iCloud Backup.