Will my Apple Watch SE 2nd gen work with iPhone 15 after upgrading to iOS 26.1?

Yes, it should continue to work just fine.

I updated my phone to 26.1 (Iphone 13) and then my watch (SE) to 26.1 The Music app is worthless now. I use my watch disconnected from my phone with downloaded music. It will not play more than 1 or 2 songs at a time in the Music app before it just quits advancing to the next song. The on-watch controls, like next, previous, pause and play will work for about 5 or 6 presses and then just become non-responsive, eventually causing the whole app to crash. There are serious problems with the Music app on the watch post 26.1 upgrade. Avoid it.

Fix to unusable Music App after 26.1 update on Apple Watch SE: I did a complete unpair and repair of my watch and the Music app is now stable. I re-paired as a completely new watch. I had to completely setup the watch and redownload music to it.

Previous Music app symptoms that all seem solved now:

1) would get spinning wheel when I entered into a playlist. Only way out was to force quit music and go back in

2) the music controls on the watch face, play, pause, next track, last track would quit responding after 5 or 6 pushes, although they WOULD give you the visual indication that the push had registered, and then the music app would crash entirely.

3) once music was playing it would rarely advance to the next song more than once. You would have to click the next song to get it to play.

4) all crashes of the app resulting in completely losing track of what track was played last, what playlist you were in, etc...

All of the above was happening when playing music that had previously been downloaded locally to the watch from and Iphone, but the iphone was not around during playback.

Since unpairing and re-pairing the watch the music apps works as expected and the problems above have disappeared.