Hi, my name is Neil, and I'm a Windows 10 user like you.
I'll be happy to answer your question.
I too suffer from this multi-tab-video-playing event most days! I have to rush through and click pause on everything quickly. It even plays videos that were paused on websites like Discovery+ and other sites too (it did that this morning :D ).
Unfortunately, as of yet, there is no way to boot up, open your browser back to where you were and have these videos paused where you left off.
This is a browser issue more than a Windows issue, so what I would suggest you do is contact Google about Chrome by clicking on the 3 dots in the upper right corner of the Chrome window and then go to Help > Report an issue
You can describe the issue in detail here and send it directly to the Google team.
Likewise, for Edge, click on the 3 dots in the upper right corner of the Edge window and then go to Help and feedback > Send feedback and do the same here and send what's happening to the Edge development team.
Hopefully they will be able to fix some code with the browsers that bring these tabs back with a paused state on any video media.
I hope this helps.
Kindest regards,
Neil