How does Apple Watch backup work?

Yes, the Watch uses basically the same mechanics as the iPhone, since it more or less piggybacks it's backup with the iPhone's backup.

In your given example you would likely want to first unpair the Watch in the Apple Watch app on your iPhone. You might notice that the unpair process takes a while (a minute or two) compared to unpairing of other bluetooth devices, this is because the Watch automatically backs up to the iPhone when unpairing is initiated. When you pair the Watch back to the iPhone you will be prompted to set it up as new or restore from a backup, similar to how an iPhone asks when you first set it up.

Source - Just had this conversation with an Apple Genius yesterday when dropping my Watch off for service.

This Apple KB article explains this as well - HT204518 Back up your Apple Watch

Even on iOS 14 and watchOS 7, there is no good indication a watch backup ended or worked. No way to view if a backup is done, no warning when backups fail, and no warning if backups don’t happen for extended periods.

I have to keep a second watch around (or borrow it from a friend) to try a restore to even see if my watch backup is viable.

Every other device is a first class citizen with date and time in iCloud settings. It’s odd the watch, which contains your most personal data, isn’t logged as being backed up.

Apple Watch backups seem to be far more fragile than iOS backups to iCloud. For example, since learning that I can check the backup status on my iPhone in Settings.app > General > Storage & iCloud Usage > Manage Storage under STORAGE and not under ICLOUD > scroll all the content up, again and again to find Watch (usually the smallest item so it's at the bottom of the list)

My watch hasn't backed up since 9/10/15 and I get no warnings, no errors, no backups since Watch OS 2.0 was loaded on my Watch. iOS 9.0.1 hasn't improved things.

I recommend checking on this and requesting support from AppleCare if you don't see backups happening every day. There should be better feedback and an easier way to know your watch is backed up plus some sort of noticeable warning when daily backups are missed for days or weeks at a time.

My devices all back up to iCloud and never seem to be more than a day between backups (sometimes they even back up in the middle of the day without asking - YAY) but the watch backup seems exceedingly fragile in my experience.