[Studio] feat: stream AI chat responses

[Loyal-Young]

Summary

• replace the AI page's simulated delayed reply with the backend SSE chat stream
• append streamed chunks to the in-progress assistant response and retain a stable conversation identifier
• add a stop action, cleanup on unmount, and user-visible failure feedback
• align the chat request type with the backend's optional conversationId field

Validation

• npm.cmd test -- ai.test.ts
• npm.cmd run lint (5 existing warnings, no errors)
• ./node_modules/.bin/tsc.cmd -p tsconfig.app.json --noEmit
• npx.cmd vite build was attempted but timed out without diagnostics on this Windows host.