What a strange confusion, as if all people must have the same "workflow". Sorry, no intent to sound negative, but why not give it some thought at least. It's "6 tabs", not "6 videos playing at the same time".
This seems intentionally YouTube's UX design fault, they too heavily try to push you to "auto-play". YouTube has a "Watchlist" feature where you can build a playlist. When it works it is exactly what I want, but it feels like every so many months it mysteriously breaks for a while or they hide the button for it behind some new hidden gesture or menu they expect you psychic out of their UI. (If you've never heard of "Watchlist", no wonder. It seems intentionally hard to discover.) Lately I've been complaining that YouTube adds random "auto-play" videos even to a manually curated "Watchlist" if you don't pay enough attention or watch past the end of the list (even with auto-play and recommendations entirely off).
I’m still using Watch Later, but for long videos I have no time for.
I expect YT is probably doing some preloading or heavyweight running in a loaded-but-not-playing tab.
Convert that to load-on-click, and you'll likely fix your issue.
The fact is, it doesn’t happen in Chrome for “magical” reasons, according to a comment few levels up. And regular non-tech users won’t debug this with click to play or whatever. We expect that YT does it absolutely intentionally.
It bends userbases however it wants due to its multi-dimensional reach, and we’re like “hmm maybe extension would help prevent accidental preloading issue”. I just don’t get it.