Add resizable room panel, searchable user picker, and direct room membership

Room info panel is now user-resizable (fixing a layout clip at narrow
widths), and every user-selection spot (room membership, admin ownership
transfer) uses a new searchable UserPicker instead of raw text input or
prompt(). Member rows fold role + actions into a single inline dropdown
instead of a row of buttons, so the member list stays usable as rooms grow.

Room invites (the accept/decline flow) are replaced by adding a user to a
room directly -- an admin/owner picks someone and they're a member
immediately, with a "you've been added" notification email instead of an
invite email. Drops the now-unused room_invites table.

backend/app/main.py

@@ -11,7 +11,7 @@ from redis.asyncio import Redis
 from starlette.middleware.sessions import SessionMiddleware
 
 from app.config import settings
-from app.routers import admin, auth, bots, health, invites, push, rooms, signup, users, webhooks
+from app.routers import admin, auth, bots, health, push, rooms, signup, users, webhooks
 from app.ws.broadcaster import RoomBroadcaster
 from app.ws.chat import router as ws_router
 from app.ws.connection_manager import ConnectionManager
@@ -75,7 +75,6 @@ def create_app() -> FastAPI:
     app.include_router(signup.router)
     app.include_router(rooms.router)
     app.include_router(users.router)
-    app.include_router(invites.router)
     app.include_router(push.router)
     app.include_router(admin.router)
     app.include_router(bots.router)