refactor(agent-streaming): Use Genkit beta client library

[agduan]

Replace Fetch API with Genkit Beta Client library to call Genkit flows

[gemini-code-assist]

Code Review

This pull request refactors the streaming flow implementation to use the Genkit Beta Client library. On the frontend, manual SSE stream parsing is replaced with the streamFlow helper. On the backend, the /api/chat endpoint is updated to match the expected protocol by accepting data instead of prompt, wrapping chunks in a { message: chunk } structure, and appending the final result. Feedback suggests checking res.writable before writing error details to the response stream to prevent potential unhandled exceptions if the client aborts the connection.

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