No, Play Store does not require Play Services integration, nor does it mandate any trackers.
In practice though, most use Play Services for lush 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.
Because you should have your email, password manager, and authenticator be 3 different services. Otherwise there is 1 point of failure.