Okay, ignore the video file part! (Especially because that’s too hard.) So find a YouTube video you like. Pause the video (I’m working from my phone — hopefully the iPad version is similar) and tap the little arrow at the top.
You should see something like Copy Link.
Tap that, go to Medium, tap where you want the video to appear, then tap & hold and select Paste.
The address (URL) of the video appears, but no video.
But when you tap Return to start a new line, BOOM! Medium fills it and you have your link into YouTube:
Hope that helps?