I used to do something similar when I was into cracking (as a hobby), to watch series on Netflix/Amazon Prime without actually paying for it.

(It's probably illigal right?)
Actually I can't say whether using someone else's cookies is legal or illegal but since nobody was harmed because you used them we can't blame you. I know you're not a hacker so someone must have given you those cookies.
I'm thinking what if the people who collected these cookies also collect cookies from the Bitcointalk forum in the same way (I don't know how they collected them maybe the previous method no longer works).
Our biggest problem is that we always log in to the Bitcointalk forum with the 'Always stay logged in' option checked. Because of this if we forget to log out the account stays logged in on that browser forever. If we log in by selecting a specific time period instead I think we will never face this kind of problem.
Yes, no harm was done, I only watched a few movies without disturbing anyone!

As for the logs that's a mystery for me as well, I don't know the process. But there are many telegram groups, certain commuity or forum where these logs can be found. Most of the juicy stuffs are paid though. And they charge good amounts for these leaked data.
Forever isn't literally forever you know! it's 3153600 minutes (or hours, can't remember exactly which). That's already a long time, but it's not forever. You cookie session would always expire (eventually afaik).
Try to login with wrong credentials but make sure to tick the "Stay Logged In" box, you'll see 3153600.