feat(firebaseai): server prompt chat and function calling

[cynthiajoan]

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[cynthiajoan]

/gemini review

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Code Review

This pull request introduces server-side template chat functionality with function calling capabilities to the Firebase AI example app. Key changes include adding FlutterFire configuration, refactoring function calling utilities into a dedicated file, and implementing various chat sessions and UI elements for different function calling scenarios (auto, client override, stream). The core library now includes new TemplateChatSession and TemplateTool related classes, and model request methods have been updated to support these new parameters. Review comments highlight critical null-safety issues in TemplateChatSession.sendMessage and sendMessageStream where _autoFunctions is used without proper null assertion, potentially leading to compile errors or runtime crashes. Additionally, a high-severity bug was found in _serverTemplateUrlContext in server_template_page.dart where a user message is added twice to the UI, causing duplication.

[Lyokone]

Same as Paul, the modifications shouldn't be required, but other than this looking good 👍