Requested feature overview description.
Right now, site relies on <video> HTML tag to embed the video, meaning that the player is also handled by users browser.
It would be better to have customized video player with all the available options in it.

Why would it be useful?
Right now the player is inconsistant to all users using differend software and even updates of said software (user using differend mobile vs desktop browsers, old edge vs new edge, etc.). Addition to this, some software lacks some features others have which are still supported, e.g. playback speed. We have had users uploading e.g. speed up/slow down edits of animations in past because they didn't have such options.
This could also make the video player fit in more on the sites themes and possibly even have video sample selection directly on the player in addition as many seem to not notice the dropdown below the video.

What part(s) of the site page(s) are affected?
WebM (and in future all other video formats) posts.

mairo said:
Addition to this, some software lacks some features others have which are still supported, e.g. playback speed. We have had users uploading e.g. speed up/slow down edits of animations in past because they didn't have such options.

I'm personally using a playback speed-adjusting extension on my browsers for some videos that are animated too slowly for my liking.

Couldn't a user get a browser extension to display standard video elements as they want, if the standard browser-supplied controls aren't good enough? A custom video player would get in the way of behaving as other normal video elements, and while I'm not a web developer to know why, most sites I've seen with a custom video player seem to have worse performance than a normal video element.

Gotta say I'm not keen on this idea either. If I don't like the feature set of the browser's video player, at least it's within my power to do something about it. A custom player would take options away from me and, as Watsit said, is pretty likely to be a downgrade anyway.