A tip: in a browser, one can replace the "shorts" part of the URL with a "v", then watch it like a normal video with all the controls there. It's true for YT, at least.
Example. Before conversion
After conversion (browser will automatically rephrase the syntax of URL)
Note how Medium treats these two forms of embedded link differently: in the former case, there is no embedded player window at all, whereas in the latter it emerges.
The end result is still objectively ugly, but one gets progress/nav bar, which is better than absence thereof.
PS tested in action, just to check whether Medium app for Android breaks something, as is its habit concerning responses. Indeed, it breaks, in a sense that I had to transfer the screenshot on my laptop to insert it into response, because an attempt to add it directly from an app, as usual, ends in error. I can’t fathom why is it so only for responses, but not for stories. But the transformed URL is treated correctly by app, and player is working.
