Results are showing above the auto-complete complete - this is fine.
But when I type something that's not in the suggestions list, the dropdown gets rendered below the input. Shouldn't it be rendered above the auto-complete input as well?

I think is rendered dynamically, based on how large the dropdown is. I don't know if you'll be able to force him to render in one direction. For dialogs at least, it would be best if the large list was rendered below the input as well.
This above-the-input rendering is our own implementation, so we should be able to make the "No results" render above as well.
P.S. Initial idea was to have this dropdown show below the input at all times, but it gets cut off by the parent overflow:hidden container. Altering that CSS prop then introduces other mindblowing issues.
Most helpful comment
This above-the-input rendering is our own implementation, so we should be able to make the "No results" render above as well.
P.S. Initial idea was to have this dropdown show below the input at all times, but it gets cut off by the parent
overflow:hiddencontainer. Altering that CSS prop then introduces other mindblowing issues.