The <amp-youtube> extension supports embedding an individual YouTube video but how do you embed a YouTube playlist on an AMP page?
Well, you cannot use the <amp-youtube> to embed a YouTube Playlist. The <amp-youtube> is only used to embed a single/individual video.
A playlist in YouTube has this following form.
https://www.youtube.com/embed/videoseries?list=PLlVlyGVtvuVll4Te_6kO4CsI7dcPJKQLt
So instead of <amp-youtube>, try to use the <amp-iframe> with it and check if it works.