There's a very outdated notification system where you can 'subscribe' to a thread for notifications through email, but that doesn't even work in my experience.

I think a better idea would be to have something more like an actual pop-up notification on your browser that could maybe even be added ingame. So if someone were to quote your reply or reply to a thread you'd made you'd be able to respond quicker.

I dont see why not making it a option to enable and disable, and we have something alike for private messaging (a pop up)
supported