refactor: remove api-types.ts compatibility layer

- Migrated all 29 files from api-types.ts to use reflector-api.d.ts directly
- Removed $SourceKind manual enum in favor of OpenAPI-generated types
- Fixed unrelated Spinner component TypeScript error in AuthWrapper.tsx
- All imports now use: import type { components } from "path/to/reflector-api"
- Deleted api-types.ts file completely

www/app/(app)/rooms/_components/RoomCards.tsx

@@ -12,7 +12,9 @@ import {
   HStack,
 } from "@chakra-ui/react";
 import { LuLink } from "react-icons/lu";
-import { Room } from "../../../lib/api-types";
+import type { components } from "../../../reflector-api";
+
+type Room = components["schemas"]["Room"];
 import { RoomActionsMenu } from "./RoomActionsMenu";
 
 interface RoomCardsProps {