Avoid Firestore-reserved session metadata key in ADK Web UI

[kkj333]

Summary

• Rename the ADK Web UI's internal session metadata state key from __session_metadata__ to adk_session_metadata for new writes.
• Preserve backwards-compatible display-name reads by checking adk_session_metadata first and falling back to __session_metadata__.

Test plan

• node --check src/google/adk/cli/browser/main-TCIQIOZ3.js
• Targeted string checks confirmed no creation object, state delta, or create-session payload writes __session_metadata__.

Related to #5539

Made with Cursor

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Hello @kkj333, thank you for your contribution!

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Thanks!

[kkj333]

Closing this for now. The issue is likely best fixed in the ADK Web source repository and then propagated into this bundled asset. I will wait for maintainer guidance on #5539 before opening another PR.