The Youtube notifications are absolutely terrible though. They stick around after the streamer is done, so every time I open YouTube I get notifications like "someone is live!" when the stream ended 8 hours ago.
They stick around because by default ended streams hang around as a video and so you can watch it after the fact. Maybe they need to update the notifications so it can say "someone was live x hours ago"
Yeah but you don't seem to get notifications for people just uploading a plain old video either (at least not by default, unless I accidentally changed something).
I think there is a little bell icon next to the subscription button. If you check it videos send notification too. There is an option somewhere where you can choose which things send you notifications.