My wife has an Apple Watch SE A2351 and it is saying it is up to date as of 10.6.1 and I cannot find anything saying if it should/can get 11+ or not.
So the Apple user guide for watchOS 11 lists the available models. If you were unsure about which gen SE you had, you would have to check their identify page. Links below.
From what you posted, you have a the first gen SE which doesn’t get watchOS 11.
I wish they had a comparison chart but I can’t find it if they do.
https://support.apple.com/en-ca/guide/watch/apd2054d0d5b/watchos
The Apple Watch SE A2351 is still supported but it only goes up to 10.6 according to gsmarena and Tom’s Guide
https://endoflife.date/apple-watch
https://www.gsmarena.com/apple_watch_se-10446.php
We have bad news for people with Apple Watch Series 4, Apple Watch Series 5, and the original Apple Watch SE (2020). Apple has just revealed that OS software updates will no longer be supported for either watch, taking effect with the release of watchOS 11.
you can check the table under “Version History” on the watchOS wikipedia page, the second to last column on the right has the oldest supported model for each version: https://en.wikipedia.org/wiki/WatchOS
The best I could find was an implication in an Apple [press release footnote]:(https://www.apple.com/newsroom/2024/06/watchos-11-brings-powerful-health-and-fitness-insights/) “watchOS 11 will be available this fall as a free software update for Apple Watch Series 6 or later paired with iPhone Xs or later, running iOS 18.” So effectively, as interpreted elsewhere, the original SE is out but the SE 2 is fine.
I have an SE2, and it runs watchOS 11 just fine.