fix: support A2A root agents remote templating

[allen-stephen]

Summary

• Fixes is_adk derivation to use base_template_name instead of tags, enabling remote templates using adk_a2a_base to correctly inject app object when needed
• Adds unit and integration tests for ADK app injection
• Fixes hardcoded agent name assertion in A2A template tests

Closes #450

[gemini-code-assist]

Summary of Changes

Hello @allen-stephen, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request addresses a critical issue where remote ADK templates, especially those based on adk_a2a_base, failed to correctly inject the app object due to an incorrect derivation of the is_adk flag. The fix involves updating the is_adk check to rely on the base_template_name rather than potentially missing tags. This ensures proper functionality for these templates and is backed by comprehensive new tests to validate the app injection mechanism.

Highlights

• ADK App Object Injection Fix: Corrected the logic for deriving is_adk to use base_template_name instead of tags. This ensures that remote templates, particularly those using adk_a2a_base, properly inject the necessary app object.
• Enhanced Test Coverage: Added new unit and integration tests specifically for ADK app injection scenarios, covering cases where the app object should or should not be injected, and verifying the is_adk derivation logic.
• Flexible Agent Name Assertion: Updated a hardcoded agent name assertion in A2A template tests to be more flexible, checking for the presence of a name rather than a specific string.

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[gemini-code-assist]

Code Review

This is a solid pull request that effectively addresses the issue with remote A2A templates by correctly deriving the is_adk flag from base_template_name. The core logic change is clean and well-supported by a comprehensive set of new tests, including unit tests for the specific logic, behavior tests for app injection, and a new integration test for the end-to-end flow. These tests significantly improve confidence in the fix. I have one suggestion to make the new integration test assertion more robust.