I wrote a user script that does that!
Available on my GitHub, on Greasy Fork and OpenUserJS, under the MIT license.
What it does
It checks if it's on a video page (URL contains /videos/) and if so:
It checks every half a second if the popup appeared, and if so - removes it.
It also cancels the next video from playing automatically.
The code snippet
If the video is made available to a custom list only, then the ability to download and/or share are removed from the basic interface.
That being said, there is surely a way for someone who has access to the video to hack and get a copy of it and then redistribute it on their own, but it is not done easily or through the normal usage of the facebook ...
With the browser extension: uBlock Origin (Chrome version / Firefox version), AdBlock Plus, or a similar content-blocking browser extension that can use AdBlock Plus syntax filter lists, you can add the following custom filter:
That should block the "up-next" video autoplay and pop-up.
After searching the web for few hours, apparently there is no current way to disable that feature.
There are some question threads on Facebook's help community that are a few months old, as like the one in the link and none of them got answered by Facebook yet.
How can I turn off the "up next" video feature?
I don't think this is a new feature unless I'm missing an announcement somewhere.
You can just use https://www.facebook.com/search/USERIDHERE/videos-uploaded
or in search phrase format "Videos uploaded by NameofUser"
"Videos uploaded by Mark Zuckerberg"