What is Firebase App Indexing Under Google Services Settings

Firebase allows developers to mobile and web apps that provide a database, analytics, cloud messaging, authentication and more without the need of sever side functionality. It belongs to Google.

From Connect to Firebase:

Firebase is a mobile platform that helps you quickly develop high-quality apps, grow your user base, and earn more money. Firebase is made up of complementary features that you can mix-and-match to fit your needs, with Google Analytics for Firebase at the core.

The indexing is the database collecting apps' information that will later be analyzed (apps that installed on the device that use Firebase API): user interactions with the app, what they click, see, etc.

Where do all these data go ?

They are stored on Google cloud stores.

Is this a privacy issue ?

Yes, it can be a privacy issue when the apps using the Firebase API collect too much information that are not related to the app's main purpose. Don't give too much permissions to apps. If necessary, write to the developers to ask why they need certain permissions for their app(s) (if they did not list or elaborate on their Google Play Store page).

Firebase documentations are found here.