When making an educational video, does citation need to be in the video itself?
The big disadvantage of citations that are part of the video itself is that they can't easily be a link, or even copy-pasted into a search engine like a text citation. So if it's a URL, the viewer will have to pause the video, and type the URL manually. You could use YouTubes "cards" function to add links as pop-up interactive overlays, but I think you are limited to 5 links per video.

I would put my citations in the description, and in case the video gets embedded somewhere else, give them at the end of the video as well, perhaps with a link to a page where they could be found.

There is no set convention that I know of, unlike citations in papers or books. There is a podcast that I listen to that does give citations, but they just tell you how many at the end and send you to their website to read the transcript to find them. I don't think most viewers are expecting them, except for the implicit citation you give when you say something like "in a 2019 study by Dr Stib, it was noted that…" when citing other's research.