Phase 1: auth, room CRUD, WebSocket chat, PWA frontend

Invite-only FastAPI + SQLAlchemy(async) + Postgres backend (session-cookie
auth via CLI-provisioned accounts, open-room CRUD, single-instance /ws/chat)
and a React + Vite PWA frontend (login, room list, chat view). Backend tests
pass against a local Postgres DB. See README.md and backend/README.md for
setup, and ARCHITECTURE.md for the full phased design.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/models/room.py

@@ -0,0 +1,25 @@
+import uuid
+from datetime import datetime
+
+from sqlalchemy import Boolean, DateTime, ForeignKey, String, Text, func
+from sqlalchemy.orm import Mapped, mapped_column, relationship
+
+from app.models.base import Base
+
+
+class Room(Base):
+    __tablename__ = "rooms"
+
+    id: Mapped[uuid.UUID] = mapped_column(primary_key=True, default=uuid.uuid4)
+    name: Mapped[str] = mapped_column(String(100), unique=True, index=True, nullable=False)
+    description: Mapped[str | None] = mapped_column(Text)
+    is_private: Mapped[bool] = mapped_column(Boolean, default=False, nullable=False)
+    owner_id: Mapped[uuid.UUID] = mapped_column(ForeignKey("users.id"), nullable=False)
+    created_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True), server_default=func.now(), nullable=False
+    )
+
+    owner = relationship("User")
+    memberships = relationship(
+        "RoomMembership", back_populates="room", cascade="all, delete-orphan"
+    )