Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
I've tried. It even says I have 2.7 available, but apparently it's not quite there. It was such a pain getting it to work the last time. Ridiculous that Apple would still support, much less sell, watches that are so close to the memory threshold that an empty watch can't be updated.
 
Another thing to consider - I noticed that, even after unpairing and setting up my Series 3 as a new watch, I would start with > 3Gb available, only to have the upgrade consistently fail. The upgrade reason was strange - “the upgrade cannot be verified because your Apple Watch is not connected to the internet”, even though it was. After this happened a number of times, trying different combinations of Bluetooth and WiFi on/off, I noticed that I had zero memory on the watch, and that my Music app had expanded to 1.5 Gb. That’s when I noticed a setting on my iPhone watch app “Music->Recent Music” which automatically adds new music to your watch. This must be a default setting, because I don’t ever remember checking this and never set up any playlists to download to my watch. So, it appeared my iPhone was slowly adding music to my watch during the upgrade, until the watch ran out of memory!

Long and short - when I turned off this setting, the 3Gb I had recovered from pairing and setting up as a new watch remained available and the install of WatchOS 7 (7.2 in my case) was successful. Quite the road to get there, though!
 
Initially, I got the same error on my S3 (which was a bit of a surprise because I wasn’t aware 7.2 was coming out !).
However, I just tried updating direct from within the watch (normally I initiate from my phone app) and everything downloaded and installed without a problem !
Thank you for posting this! You saved me the pain of pairing/unpairing again. Hopefully others see this so they realize how easy it can be.

On Apple Watch S3 (not your iPhone!), go to Settings > General > Software Update. As Graham4723 said, initiate the update from there on your watch. Then put the watch on it's charger and find something to do for an hour or so. Obviously, if you care about your fitness streaks, make sure to get your stand in at the top of the hour and then do a back-up to iCloud and then do the update.
 
Things I had to do: Unpair => Repair as New Watch => Immediately Update to new iOS => Unpair => Repair with old back up.
Wish I had tried the update via the watch instead of the iPhone Watch app though!
 
Just to say, I again used this method to update my S3 to watchos 7.3 yesterday.
No unpairing/repairing etc. Put the watch back on the charger and update completed.
 
Things I had to do: Unpair => Repair as New Watch => Immediately Update to new iOS => Unpair => Repair with old back up.
Wish I had tried the update via the watch instead of the iPhone Watch app though!
Don’t worry. It didn’t actually work for most people. Unpairing didn’t even work for me.
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.