Recommend downloading APK Grabber from GitHub. It'll check for updates to system apps on APK mirror. The ones you want will say mainline in the name. The permission manager is another and so is captive portal. I don't recommend it because you'll have to manually update from here on if you do.
But if you want to then the link to APK Grabber is here.
You dont need a phone to play or use the emulator, that being said if you are getting that error on the playstore probably means that the device the store is seeing (the one being emulated) isnt compatible not a big deal easiest way to work around is going to apkpure and download the game apk from there (apkpure is a safe source of clean apps) grab the apkgrabber from this link and in settings enable google play store and apkpure, this way you can easily update the game in the future.
You could try an app called APKGrabber to notify you of the releases.
You could parse the RSS feed to look for changes in the version number.
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I don't think there's any way to download the apk directly.
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