End result, I have to burden the server with a massive, crappy looking GIF after trying a dozen formats. With all due respect, this is worse than some aging service like Reddit that doesn't support new media formats.
For reference, I'm using the web interface. Is this just a format restriction of lemmy.world, or an underlying software support issue?
You generally can embed them the same way as you would a gif with the  format
That's how I just embedded this mp4.  Works fine on desktop/web, is a bit broken for phone apps, depending on the app.
You should probably talk to the devs, as I'm pretty sure this is just how Lemmy works. It's not very format-friendly, on any instance. But then I think they want to center text as more important than images/video.
Also, storage space is expensive, so I think they're trying to minimize impact to admins who have a bunch of throwaway media uploaded to their servers to be viewed once and then never again.