feat(genai): add migrated functionCallingStreamContent sample from generative-ai

[angelcaamal]

Description

This PR introduces tool-func-calling-stream-content.js, which is the version already migrated from Vertex AI to the new genai standard, applying the proper name change and region tag following the naming convention of the samples under genai.

The primary reason for this migration is to phase out the legacy functionCallingStreamContent.js sample and decommission its old region tag on Devsite, replacing it with this updated implementation.

Fixes #

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Checklist

• I have followed guidelines from CONTRIBUTING.MD and Samples Style Guide
• Tests pass: npm test (see Testing)
• Lint pass: npm run lint (see Style)
• Required CI tests pass (see CI testing)
• These samples need a new API enabled in testing projects to pass (let us know which ones)
• These samples need a new/updated env vars in testing projects set to pass (let us know which ones)
• This pull request is from a branch created directly off of GoogleCloudPlatform/nodejs-docs-samples. Not a fork.
• This sample adds a new sample directory, and I updated the CODEOWNERS file with the codeowners for this sample
• This sample adds a new sample directory, and I created GitHub Actions workflow for this sample
• This sample adds a new Product API, and I updated the Blunderbuss issue/PR auto-assigner with the codeowners for this sample
• Please merge this PR for me once it is approved

Note: Any check with (dev), (experimental), or (legacy) can be ignored and should not block your PR from merging (see CI testing).

[gemini-code-assist]

Code Review

This pull request introduces a new sample script and its corresponding test file to demonstrate function calling with streaming content using the @google/genai SDK. The review feedback highlights critical corrections and improvements: the role for the function response turn must be changed from 'user' to 'tool' to prevent API validation errors, and redundant nesting in the function response structure should be simplified. Additionally, the test file should default to 'us-central1' instead of 'global' since Gemini models are regional on Vertex AI, and the script path in the test should be resolved dynamically using the path module to ensure directory-independent execution.

[snippet-bot]

Here is the summary of changes.

You are about to add 1 region tag.

• genai/tools/tools-func-calling-stream-content.js:15, tag aiplatform_genai_function_calling_stream_content

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