FWIW, you can install the entire proton suite with Obtainium. For whatever reason though, 1password exclusively distributes through the Google play store, but AFAIK that doesn't make the app itself any less private.

No, Play Store does not require Play Services integration, nor does it mandate any trackers.

In practice though, most use Play Services for push notifications, and there are a LOT of apps with at least Google Crashlytics, Google Firebase Analytics, and Google Admob trackers. Check out Exodus for tracker reports. Or use the Tracker Controller app. Just note that some trackers are pretty benign, or even a security feature, like Sentry.

Aurora should actually say in the description of the installation/update screen if the app requires google play services or any telemetry at all (or for that matter, google sign in).