Project Thumbnail Videos work fine outside a Carousel but you are right that when within, the project Thumbnail defaults to the Image. The Slides are "Behind Glass" in a way in that the Hover does not affect the inside.
Sorry that my answer doesn't get you any further, this would need to be Custom Coded and you may wish to ask a developer to do this.
These Links may help:
https://stackoverflow.com/questions/16000443/how-can-i-make-an-image-become-an-embedded-video-on-mouse-over
http://jsfiddle.net/3SQtS/
https://stackoverflow.com/questions/26082409/change-inner-html-on-hover
The Slides have an Image element <img> inside of them:
Screen Shot 2021-12-14 at 4.17.50 PM.png
There is slide-inner as the parent and within as it's child the img class="carousel-img". So the step would be to use Javascript or JQuery to take the <img> and replace it with a <video> on Hover (mouseover or mouse-enter).
Best wishes ✨ Richard