Download embedded private Vimeo video with yt-dlp
yt-dlp --referer "<url-of-site-which-embeds-video>" "<vimeo-url-from-page-source>"
e.g. yt-dlp --referer "https://www.somesite.com/" "https://player.vimeo.com/video/1234"
For Dockerised yt-dlp: docker run --rm -it -v "$(pwd):/downloads:rw" jauderho/yt-dlp:latest --referer ...
It should be possible to pass a cookie if one is required to load the referring page (have not tested yet).