I tried setting the length of the iframe where the Discover screen appears, but the Discover screen ignored it and the display was still incorrect and way too short. It still briefly displays correctly before showing the thin window that is not usable.
I found the global setting doc_table:legacy and set that to true, and my embedded Discover screen immediately started working. So the new Discover screen does not work when it is embedded. I can understand why this wasn't tested because the Discover screen doesn't have a Share -> Embed menu option like the dashboards do. But we've been embedding dashboards and the Discover screen the same way for five or six years and the new Discover screen does not display when embedded.
Since the legacy version is embed-able and the new version functions correctly in that you can browse data, but can't embed and display that data, I still say that this is a bug.
And this Advanced Setting cannot be configured via my kibana.yml file. Is this forum post from 2016 still true? It doesn't seem to work for me, possibly because the API has been deprecated.