Discourse is quite a clever platform. Once you have replied to a thread and there are new posts you will get to see these and it even scrolls you down to the unread items.
My personal method is to use the hamburger menu in the top right and select ‘New’ or ‘Unread’ to get a quick view of changes.
There is also a Discourse mobile app but I have not got much experience with that. Maybe worth a look.