I tried Syncthing and it worked really well and it was fast. But I definitely want to have a webui, like Nextcloud, that's why this is sadly not an alternative for me.
(Though I use syncthing now for other stuff, where I don't need web access)
I'm in a similar boat, where I use NextCloud but really wish there was a better option (especially for mobile photo sync). Syncthing + Photoprism is currently at the top of my list of possible viable alternatives.
I also tried Immich, but it just didn't work well.
I think I didn't try out lychee, but I took a look at the demo site, and it seemed a bit to minimal for me.
Though I'll definitely keep an eye at these galleries, as I don't think Nextcloud will improve their UX in this regard.
Syncthing seems to be by far the best solution for synchronising files, I just wish there a gallery that would suit my needs. If I was proficient in frontend development I'd already have created one.