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With google restricting the permissions i've installed the same versions from this website, over the top to keep restrictions intact. So for now the app is still "linked" to google play. Now i'm wondering, what will the impact be of updating? Will GP update the app grabbed from the site or are the signing keys different?

Do i need to disable updates for the app?
Do i need to uninstall, then reinstall the site downloaded app? If so, what is the update procedure (or what will it be) and will the app "link" itself to GP?

With this site downloaded version, perhaps it's an idea to build in a version checker that detects new versions on the website and notify in-app/through notification. Perhaps also use different signing key's so the app won't link itself to the play store, until permissions can be fixed (API)? "Do Not Disturb" from Cabooze Software (on the play store)

From it's changelog

Changes to support Google's restricted CallLog and SMS permissions. Latest version 2.53 disables SMS sending capabilities, as well as call filtering based on incoming caller ID. On the plus side, it's now using the filtering based on Favorites, and should be very stable on wide range of devices. We exploring a way to bring the more flexible call filtering and SMS auto-responder back. Stay put.

It's doing that "filtering based on favorites" through an api the ingame changelog sais. Perhaps you could use the same API to keep number recognition.

IF there's anything you want me to do? Do let me know, i'll be happy to use a test version (Nexus 6P and Pixel 3 XL)

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The version in our website uses the same signing key as the version in Google Play.

If you previously installed the Google Play version, you can directly install the version from our website to overwrite it. All your settings and data remain unchanged.

When we publish a new version in Google Play, at this moment Google Play will automatically update the app in your phone to the Google Play version. We are considering how to deal with it.