You can have upward in any direction, but the labels are drawn in the texture and do not change when the map is rotated.
There is only one way to work around this (regardless of the provider you are using) - disable labels, read labels from vector tiles, and display them using TextMesh.
Online Maps can read vector tiles, but cannot display them, so (at least in the current version) you will need to implement this yourself.

The UI Compass demo scene lets you rotate an already-rendered map, but does not re-render the map with a new "up" direction (so that labels are always oriented horizontally).

This question is specifically about using Google Maps... but if it turns out this functionality is only possible with a different map provider, we may consider a switch. This seems to be possible in the Google Maps mobile app, so I'm guessing there's a decent chance this is possible?