In the past we could embed YouTube videos without cookies by simply pointing to a different URL, so for example https://youtube-nocookie.com/embed/sRrqF8eXs38 to get the version
Use the www version, that works perfectly fine: https://www.youtube-nocookie.com/embed/sRrqF8eXs38
That is the version their automatic code generator outputs as well, when you chose the extended privacy option.
Looks like they removed the non-www version for some reason. (Although doing that without adding an automatic redirect would be kind of a weird move. Perhaps it is just a temporary problem or error.)