The big tl;dr is that a lot of stuff will work, but a lot of things relying on historical data will not work (resting heart rate, weekly step count, sleep, etc).
But, the app/account is unobtrusive to the point that you could name yourself Mickey Mouse on creation, just to get a user ID for the watch to point to, and set permissions on the app on some schedule just to have the watch sync that data.
No sort of verification/authentication of identity at account creation and the app/services are free (I’m sure, given this day and age, there’s premium/subscription stuff but like I said it’s unobtrusive and I’ve never once been nagged to upgrade my account)
I have a Garmin for trail running, but it has a compass, offline maps, barometric altimeter, bunch of other stuff. I used it to plan a 2000 mile route through Canada while driving last summer because my phone had shit-tier 2G/3G roaming. I have it scheduled to go into ultra battery conservation mode when I should be sleeping and only need to charge it every 2 weeks.
It also records activities even without a phone, just need internet to upload it to Strava later, so pretty handy to be able to run without a phone (Strava or it didn’t happen lol)
I have the Fenix 6X, which normally lasts 4-5 days with all bells and whistles enabled. Three settings I use to extend the battery to 2 weeks:
Disabled backlight on gesture, kept backlight enabled on keypress, set backlight to 5% and 4 seconds.
Disabled SPO2/oximetry (huge battery hog and doesn’t ruin functionality of other things to disable)
Battery Saver set on a schedule for 10 hours per day - disables wifi/bluetooth. Basically an extreme ‘do not disturb’.
But the two week figure is when I’m not doing many if any activities. Every other Wednesday it gets to around 20% and I charge it, but when I was running a lot it was closer to once a week.
Fenix 7 apparently has even better battery life tho so you might be able to wring 3 weeks out of that thing