Fix Gemini generation config for PaLM2 support

[jonahsills]

/claim #279

Summary

• Fix the existing Gemini/PaLM-compatible provider so generation options are sent in Google's generationConfig request body instead of the Axios config object.
• Export Gemini request/response TypeScript types and add a Palm2AI alias for the PaLM2/Gemini bounty API surface.
• Add mocked unit coverage under src/ai/src/tests/palm2.
• Add the required src/ai/src/testcases/palm2 Jsonnet prompt config.
• Add a runnable Jsonnet-driven examples/palm2-chat example with no hardcoded prompt in TypeScript.

Requirement Checklist

• Classes and TypeScript types added for PaLM2/Gemini API: yes
• Unit testcases under a palm2 test path: yes
• testcases/palm2 Jsonnet prompt config: yes
• Example prompt lives in Jsonnet, not hardcoded in TypeScript: yes
• Short demo included in this PR: yes
• CLA signed and CI passing: yes

Validation

• npx vitest run src/ai/src/tests/palm2/gemini.test.ts
• npm run build
• npm start from JS/edgechains/examples/palm2-chat

Demo

Short demo GIF:

The example dry-runs without credentials and prints the Jsonnet-loaded chat options. Set GEMINI_API_KEY to call the live Google Generative Language API.

Full demo transcript, included so the output remains reviewable even if GitHub clips the embedded media:

EdgeChains #279 demo: PaLM2/Gemini Jsonnet example
Prompt, model, and generation settings are loaded from Jsonnet.

$ cd JS/edgechains/examples/palm2-chat
$ npm start

Loaded Jsonnet prompt:
Explain how EdgeChains can call Gemini through a typed provider in one sentence.

Loaded model:
gemini-pro

Dry-run request:
generationConfig.temperature = 0.2
generationConfig.maxOutputTokens = 128

No GEMINI_API_KEY found, so the example stops before the live API call.
Set GEMINI_API_KEY to call Google Generative Language API.

✓ npx vitest run src/ai/src/tests/palm2/gemini.test.ts

[github-actions]

CLA Assistant Lite bot All contributors have signed the CLA ✍️ ✅

[jonahsills]

Short demo GIF for the PaLM2/Gemini Jsonnet example:

The demo shows the example loading model, prompt, and generation settings from Jsonnet, then dry-running without credentials. Live API calls work by setting GEMINI_API_KEY.

[jonahsills]

I have read the Arakoo CLA Document and I hereby sign the CLA

[jonahsills]

recheck