Currently the notifications on speedrun.com appear after refreshing the site, but I've seen on other sites that as soon as you get a notification, it appears straight away without refreshing the site. Would it be possible to implement this here, and if not, what would be problematic?

I don't see a reason to make them active notifications, personally. reddit etc. work fine the same way, as there's no urgency for those notifications. if you're browsing the site, you're not gonna sit on one page for 3 hours anyway, so you'll get the notification eventually.

While not necessary by any means, it would be a nice QoL improvement. I can only speculate on how difficult it would be to implement, but it certainly wouldn't be impossible. Would it be worth the development time/resources required to implement? Eh... probably not right now. There's a pretty hefty backlog of high-priority features as it is, so a minor improvement like this will probably stay on the backburner indefinitely. That being said, the whole notification system is being completely reworked at the moment, so who knows.

Hoype.