Discourse comment-like discussion

[Falco]

Is there a way to essentially have 1 topic dedicated to every page on our web app so that people can start independent commenting threads on each page?

Yes using Embedding Discourse Comments via Javascript

Would these per-page topics show up on the main forum topic list?

Yes

If so, is there a way to filter them out so that forum consists of only topics that aren’t page specific?

You can set the category holding those topics as Suppress category from latest topics. to not clutter the forum.