chore(vertexai): clean up chat example

[jba]

Description

Change the chat example to use more idiomatic Go.

Checklist

• I have followed Contributing Guidelines from CONTRIBUTING.MD
• Tests pass: go test -v ./.. (see Testing)
• Code formatted: gofmt (see Formatting)
• Vetting pass: go vet (see Formatting)
• 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 Product API, and I updated the Blunderbuss issue/PR auto-assigner with the codeowners for this sample
• [ x] Please merge this PR for me once it is approved

[jba]

/cc @eliben

[muncus]

aside from the minor fix noted, this looks great. Thanks!

[jba]

The CodeQL/Analyze step has the error

 Error: The configuration file "/home/runner/work/_temp/user-config-from-action.yml" is outside of the workspace

[jba]

@muncus suggestions?