This is kind of trivial because there are easy workarounds, but it seems like the same text editing is available to compose a message as for posts, but images and links work differently, i.e. not at all near as I can tell.
I was messaging with Devon and wanted to send him an image. I embedded it using the standard method and instead got something like this (I have no idea how this will pass the HTML safety code):
https://i.pinimg.com/originals/5e/1b/d3/5e1bd36536a7c5c4f63f0c54e114679e.jpg" alt="" width=“640” height=“481”>
Something vaguely similar for links.
However, if you just paste the url in as regular text, it gets turned into an active link, which is the easy work around.