Phase 2: private rooms, room roles, and invites (backend only)

Adds room_invites table + migration, owner/admin/member role enforcement
(require_room_role), and endpoints for private room creation, room
management (update/delete/leave/transfer-ownership/change-role/remove-member),
and the invite lifecycle (create/list/accept/decline/revoke). Registration
stays invite-only via the CLI from Phase 1 — this is a separate, room-level
invite system for adding existing users to private rooms.

Frontend is untouched: the UI redesign is happening separately, so this phase
is backend + tests only (35 passing). Verified no regressions in the Phase 1
open-room/WebSocket flow via manual smoke test.

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

backend/app/schemas/invite.py

@@ -0,0 +1,22 @@
+import uuid
+from datetime import datetime
+
+from pydantic import BaseModel, ConfigDict, Field
+
+from app.models import InviteStatus
+
+
+class InviteCreate(BaseModel):
+    target_username: str = Field(min_length=1)
+
+
+class InviteRead(BaseModel):
+    model_config = ConfigDict(from_attributes=True)
+
+    id: uuid.UUID
+    room_id: uuid.UUID
+    invited_by: uuid.UUID
+    target_user_id: uuid.UUID | None
+    status: InviteStatus
+    expires_at: datetime
+    created_at: datetime