A more interactive Javascript-heavy UI can improve a lot of aspects of even websites we consider to be a server-side-rendered gold standard like a forum or message board.

For example, look at the right-sidebar scrubber on Flarum that lets you quickly scroll to arbitrary parts of a long forum thread: https://discuss.flarum.org/d/17745-flarum-0-1-0-beta-8-relea...

Or look at how clicking a submission on Reddit's new UI opens it in a floating modal window so that you don't lose track of where you are when you click out of it. It makes opening submissions feel cheaper/faster to me where, in the old UI, I tended to open everything up in a new tab.

There's a more thoughtful consideration that needs to be had here than just "webapp or website?" Else you're back to cargo-culting.