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/page.tsx

@@ -16,7 +16,7 @@ import {
 } from "@chakra-ui/react";
 import { useEffect, useState } from "react";
 import useRoomList from "./useRoomList";
-import { Room } from "../../lib/api-types";
+import type { components } from "../../reflector-api";
 import {
   useRoomCreate,
   useRoomUpdate,
@@ -27,6 +27,8 @@ import {
 import { RoomList } from "./_components/RoomList";
 import { PaginationPage } from "../browse/_components/Pagination";
 
+type Room = components["schemas"]["Room"];
+
 interface SelectOption {
   label: string;
   value: string;