mine has been set to "none" this whole time, unfortunately
I figured it out for my account. The daily search quota was set to 0. I had to make a new project to get the default 10,000 quota. I'm not sure how this happened, but my API key for that project was created in 2018 and I don't think I ever used before so maybe Google set the quota to 0 due to inactivity. As soon as I got a project with the normal quota, videos started embedding correctly.
I hope this helps you as well!
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Comment by @stb109