The documentation states on a topic when to ask for a review:
Trigger the in-app review flow after a user has experienced enough of your app or game to provide useful feedback.
Do not prompt the user excessively for a review. This approach helps minimize user frustration and limit API usage (see the section on quotas).
But that's very vague, can we trigger it quite often (like after every level in a game) or should we add some wait periods inside the app (like after every level but minimum wait time a month)?
There is a similar API on iOS and it's observed that the popup shows "about three times a year". It would be helpful to know similar rough estimate, it would help to design right usage of the API and remove unnecessary user frustration.
There is no response as to whether the user rated your app or the rating dialog was shown through the In-App Review API itself. But you get these guarantees:
In case you are concerned that you might display the dialog too often, we recommend remembering when you last called launchReviewFlow
locally in a persistent way.
Let's go with your example of calling launchReviewFlow
after every level: