feat: chat prompt sample for Vertex LLMs

[gericdong]

Description

Fixes b281562687

Added a chat prompt sample for Vertex LLMs.

Note: Before submitting a pull request, please open an issue for discussion if you are not associated with Google.

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)
• 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 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

[snippet-bot]

Here is the summary of changes.

You are about to add 1 region tag.

• ai-platform/snippets/predict-chat-prompt.js:20, tag aiplatform_sdk_chat

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[telpirion]

issue: As much as I LOVE LotR and all things Tolkien (ecce my GitHub alias), we should avoid using copyrighted or trademarked strings in our samples.

[gericdong]

Agreed. Changed.

[telpirion]

issue: remove CLI per https://googlecloudplatform.github.io/samples-style-guide/#no-cli

Example of how to do it: #2888

[gericdong]

Noted. As discussed, we can handle this later with task "Remove the CLI structure from the Node.js samples for LLMs to track the changes." (b/285884334)