I made an HTML card with a Twitter widget in it to show my recent tweets and it rendered a link but not the feed. I went so far as to put the HTML into a custom layout for the card (directly, with no inclusion) and it still doesn't work:

 

http://johnabbe.wagn.org/John_on_Twitter

The layout: http://johnabbe.wagn.org/Twest

 

For comparison, I made a plain HTML file and uploaded it and that works: http://ourpla.net/twest.html