The point was that the API and URL are definitely not the issue, and the fault lies in Enbed Plus.
I used YotuWP to embed the playlist. If the issue with Embed Plus can be fixed, I may put it back. I like the features.
Just to add another troubleshooting data point, using a different embedding plugin with the same API and URL embeds the playlist successfully.
Containing element needed to have width=100% applied. Works as expected now.
