fix(core, web): skip hot-restart listener cleanup in profile mode

[SelaseKay]

Description

Profile web builds were still storing hot-restart unsubscribe functions on window. firebase_auth_web only assigns a unique listener key when Flutter's kDebugMode is true, so in profile every listener used no-op. firebase_core_web treated profile as debug because it only checked dart.vm.product, which stays false in profile. Creating FirebaseAuth subscribes to auth state and then to the ID token, so the second subscription cancelled the first before Firebase Auth could emit. authStateChanges() then never fired.

The core flag now matches Flutter's kDebugMode (!dart.vm.product && !dart.vm.profile). Debug builds still save unsubscribe functions for hot restart. Profile and release builds do not. Firestore, Storage, and App Check share this helper and the same no-op key, so they pick up the same fix.

Related Issues

Fixes #18728

Checklist

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This will ensure a smooth and quick review process. Updating the pubspec.yaml and changelogs is not required.

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• My PR includes unit or integration tests for all changed/updated/fixed behaviors (See Contributor Guide).
• All existing and new tests are passing.
• I updated/added relevant documentation (doc comments with ///).
• The analyzer (melos run analyze) does not report any problems on my PR.
• I read and followed the Flutter Style Guide.
• I signed the CLA.
• I am willing to follow-up on review comments in a timely manner.

Breaking Change

Does your PR require plugin users to manually update their apps to accommodate your change?

• Yes, this is a breaking change.
• No, this is not a breaking change.

Test plan

• Profile, release, and debug web builds of a page that subscribes to auth state and then the ID token, using the real window listener helpers. Before the fix, profile dropped the auth callback (auth js unsubscribe called). After the fix, profile emitted, with both keys still no-op and no unsubscribe call. Release and debug emitted before and after.
• dart analyze packages/firebase_core/firebase_core_web/lib/src/interop/utils/utils.dart

The flag is a compile-time constant, so a debug flutter test run cannot observe the profile branch. The full package test suite and melos run analyze were not run.

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