Settings App
and the version is shown at the top of the screen.
I was not able to search by the app name, so get ready for some scrolling.
Going under Running instead of Downloaded did not work: if you find your app there, it shows only runtime stats.
adb
The best command I found so far is:
adb shell dumpsys package com.google.android.apps.photos | grep versionName
How to get the package name: View app's full package name?
But this method is not perfect, as they can give multiple results because of the Hidden system packages: section.
Asked at: https://stackoverflow.com/questions/11942762/get-application-version-name-using-adb
Feature request for Google Play Store
Those would be ideal places for it:
https://productforums.google.com/forum/#!topic/play/CfSPJbhB6-k
Play app
I can't find this anymore on Android 16, Play App 48.6.19. It bothers me deeply as a Linux desktop guy that the thing that install apps does not show their version, but it is what it is.
Android 5.1.1 Xperia Z3:
Note: this may not work for some "magic" apps, like the Play App itself.