There are certain reasons you might be wanting to get an app update right on your android phone without installing it on your phone.
In my case, we’ve started our own apks directory on this website for the users to get the latest version of an apk/app which is the same is in play store. So downloading each app from the play store is impossible to check whether there is an update available or not.
For the first time, when I was researching for the same issue, I went to the Google console & started the discussion about the same topic with one of the google Play Store console support member. I enquired about the same issue from him that if there is any feature/option in the play store I could use to get update notification without installing the app on my device. But after the discussion, he replied me that there is no such option you can use for that purpose except downloading the app manually on your device.
Lastly, I got one small (but very powerful) app that fixed the issue in no time. Even though the google play store support member didn’t tell me about the app (I think he didn’t know about it).
Appwatcher is an android app that you can use to get an update notification for any app you choose from Play Store without installing it on your phone.
The app is free of cost & doesn’t take much space from your phone’s storage. All you need to do is just install it on your phone, connect it to any of your google play accounts & then add some apps to the watching list & you’ll get an update notification whenever there is any update available for the app you have listed in the watching list.
Feedbacks using comments are very appreciated.