I was having the same issue but found a fix from a Google forum.
A short video URL has the format:
https://www.youtube.com/shorts/<VIDEO_ID>
it also has the URL:
https://www.youtube.com/watch?v=<VIDEO_ID>
If you take the video ID and put it in the standard (2nd) format, the video can be located via Squarespace and you're all set!