yt-dlp does support "3rd party extractors" (in the form of plugins): https://github.com/yt-dlp/yt-dlp#plugins

Nope. There's two issues being talked about here. If you are in the EU then you have to provide cookies from an age-verified account. Otherwise, the age-gate bypass still works afaik. But the latter is broken in the current youtube-dl release (fixed in yt-dlp).

Also, yt-dl doesn't like yt-dlp to be mentioned on their issue tracker from what I hear.