feat: Phase 2 — web server, REST API, WebSocket/SSE, UI [v0.2.0]

AsyncEventBridge bridges sync EventEmitter to asyncio consumers.
FastAPI app with session management, discussion control, roles/providers.
WebSocket for real-time events + inject, SSE for read-only streaming.
Minimal dark-theme HTML/JS UI. `meeting-room serve` CLI subcommand.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

.tasks/v2-p2-fastapi-app.md

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+# v2-p2-fastapi-app
+
+## Goal
+Create FastAPI application with REST API endpoints for session management and discussion control.
+
+## Key files
+- `meeting_room/server.py` — FastAPI app, routes, session store
+
+## Decisions log
+- 2026-05-04: In-memory session store (dict). Persistent storage deferred.
+- 2026-05-04: REST routes under /api prefix, WebSocket/SSE on root
+
+## Open questions
+- [ ] None
+
+## Completed steps
+- [x] FastAPI app with lifespan handler
+- [x] Session + SessionStore models
+- [x] REST endpoints: POST /api/sessions, GET /api/sessions, GET /api/sessions/{id}, POST /api/sessions/{id}/start, POST /api/sessions/{id}/inject, GET /api/sessions/{id}/messages
+- [x] GET /api/roles, GET /api/providers
+- [x] Session start runs engine in asyncio.to_thread
+- [x] Tests (12 passing)