Play Store having new version of the app, but not showing update
hope this helps someone since I have benefitted a lot from this community.
If your last installed version is from Android studio, you won't see the 'Update' button in play store. You will see the 'Open' button instead. I have tested this with my development phone in which the app was installed directly using Android studio and also with some of my actual users. My users installed the last version from play store. When I pushed a new update, they see the 'Update' button in play store.
Make sure the app you have installed in your mobile is not an apk built with debug keystore. The play store will show always as "Open" button instead of "Update" if the play store app certificate doesn't match with the installed app certificate. I realized this when I did trial and error with debug and signed apk's only signed apk worked. And always use versionCode for comparing versions instead of versionName.
It also helps to clear the cache of the Play Store APP in settings. This should not be necessary. The problem is that this blocks an update to the correct version later. Only the version number is updated but not the binary. Google Play then thinks that everything is ok, but it still uses the old APK.