I’ve seen some other topics dedicated to this, but no conclusive solution. I’ve stripped down the problem to the simplest page possible:
When sharing this page on twitter, and viewing on the iOS app, the video card will continue to show the blue play button during playback. Twitter is loading and playing the “twitter:player:stream” URL, which is just a simple MP4 file. No additional page elements or meta tags are influencing this, as far as I can tell.