[cloud_firestore]: Set Dart client language header

[mit-mit]

Is there an existing issue for this?

• I have searched the existing issues.

Which plugins are affected?

Other

Which platforms are affected?

No response

Description

The Firestore package should set the API header x-goog-api-client to gl-dart to ensure Google-internal telemetry works correctly. Currently this is only done in the AI packages: code examples

One way to set this header is to use the SetClientLanguage (iOS, Android) passing in gl-dart. This is already done in the Unity package.

Reproducing the issue

n/a

Firebase Core version

All

Flutter Version

All

Relevant Log Output

Flutter dependencies

Expand Flutter dependencies snippet

Replace this line with the contents of your `flutter pub deps -- --style=compact`.

Additional context and comments

No response