I use Gmail on my Android 11 phone, not only for email but also for some other services of Google such as Maps). Due to privacy concerns, I've been thinking about installing some applications (such as Bitcoin wallets or encrypted messengers) that are offered by the Google Play Store directly from an APK package (I mean without any other store such as F-Droid, hoping that no information of the fact that such package is installed is sent to Google).
Is such information sent anyway? If it is, what other information is sent to Google about those applications (usage?)?