feat: add analytics demo example

[AbhinRustagi]

Closes #300

Summary

• Adds examples/analytics-demo, a conversational analytics chat app showcasing OpenUI's chart, table, and metric card components
• Uses Google Gemini SDK (@google/genai) with streaming and manual tool-call loop
• Includes 4 mock analytics tools (query_revenue, query_sales, query_metrics, query_customers) with built-in sample data — works out of the box with no external data source
• Follows the same structure as examples/openui-chat

Test plan

• Set GEMINI_API_KEY in .env.local and run pnpm dev from examples/analytics-demo
• Verify conversation starters render and clicking them produces streamed analytics UI (charts, tables, metric cards)
• Try multi-turn queries (e.g., "Show me revenue trends" → "Now compare by region")
• Confirm pnpm -r run build passes for all workspace packages

🤖 Generated with Claude Code

Example Screenshot:

[AbhinRustagi]

@ankit-thesys, I haven't been able to test this; it is modeled on the openui-chat example. I don't yet have an API key for OpenAI. Will perhaps need your help, or if you can allow another day.

[zahlekhan]

https://ai.google.dev/gemini-api/docs/openai
@AbhinRustagi you can use Gemini with OpenAI SDK

[AbhinRustagi]

thanks @zahlekhan for this

[ankit-thesys]

I will test it once i am little free 😄

[AbhinRustagi]

Thank you @ankit-thesys

@zahlekhan I tried using Gemini with the OpenAI SDK, in my exploration, the tool calling does not work well yet with Gemini. Gemini's streaming endpoint sends the tool calling chunks as a single completed chunk, but OpenAI SDK runTools() expects a stream of chunks because of which the accumulator loses the tool calls. I was able to write a custom tool calling loop. Do you think adding that for this project would be overkill? But happy to push it to help add it and document it since it might help someone. Would also be happy to hear if you've any experience/inputs with that

[zahlekhan]

Not needed, let ankit test it out this time.