Have you checked youtube? I don’t know how often they upload new episodes, but I run across QI all the time. And checking it again, their youtube channel is regularly uploading new episdoes and it looks like they’re up to Series (that never feels right) 20, while the actual show is in 21.
I didn’t check the other two shows.
FWIW, there’s a BBC show thread around here somewhere from when a bunch of us were watching Taskmaster/Countdown/Would I Lie To You/Big Fat Quiz etc.