I was looking for a bookmark app that can sync via Syncthing too, but I had no luck finding such an app.

I think I will end up using markdown editor (notes app), specifically Markor, because it allows appending links to a file (note) through the share menu. It's using .md files which you can easily sync via Syncthing, and then open the file on desktop with some markdown editor like Joplin.
On desktop you would have to manually copy and paste the link into the file though.

It's probably possible to streamline that process more, but if you don't save a lot of links it's ok, I guess.