The other day I had a random thought.
I wonder if there is a version of Azure Portal for Android.
Turns out there is!
This looks most useful for quick observations of machines and services, such as after receiving an alert. But as Kenneth points out, hooking a phone up to a monitor, keyboard, and mouse (which, at least on newer Samsung models, is definitely an option) means that you can hit that cloud shell and do most of what you need.