Add Google ADK generative-UI chat example

[rabisg]

Overview

Adds examples/google-adk: a Next.js app that wires a Google Agent Development Kit (ADK, TypeScript) agent to OpenUI's generative UI frontend — alongside the existing mastra-chat / langgraph-chat agent examples.

What it demonstrates

• A Google ADK Agent with a FunctionTool (weather) running in a Next.js API route via Runner + InMemorySessionService, with ADK sessions keyed by chat threadId so multi-turn history is preserved.
• The integration bridge: ADK's runAsync SSE event stream is translated into OpenAI-style chat-completion chunks so OpenUI's openAIAdapter() can parse them. Partial events stream as deltas; the final aggregated event is skipped to avoid duplication.
• Rendering the streamed OpenUI Lang with <AgentInterface /> and the built-in openuiChatLibrary. The agent is prompted with OpenUI's generated system prompt (src/generated/system-prompt.txt) so its replies are OpenUI Lang.

How to run

cd examples/google-adk
echo "GEMINI_API_KEY=your-key" > .env.local   # free key: https://aistudio.google.com/apikey
pnpm install   # from the monorepo root
pnpm dev       # http://localhost:3000

Verification

• tsc --noEmit ✓, next build ✓
• Ran the dev server: GET / → 200; POST /api/chat streams text/event-stream in the exact chunk shape openAIAdapter() expects. ADK logs confirm it created the user event and issued a streaming gemini-flash-latest request. (Model call only fails on a placeholder key — the route catches it and closes the stream cleanly.)

Notes for reviewers

• pnpm-lock.yaml gains the examples/google-adk importer plus @google/adk's dependency tree. The install was regenerated from the committed lockfile so only google-adk's footprint and the unavoidable shared peer-hash ripple (it pulls encoding into the hoisted graph) change — no other example's importer block is touched, and there are no orphaned removals (just two trivial transitive bumps: @emnapi/runtime and a postcss patch under autoprefixer).

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