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)/browse/_components/FilterSidebar.tsx

@@ -1,7 +1,10 @@
 import React from "react";
 import { Box, Stack, Link, Heading } from "@chakra-ui/react";
 import NextLink from "next/link";
-import { Room, SourceKind } from "../../../lib/api-types";
+import type { components } from "../../../reflector-api";
+
+type Room = components["schemas"]["Room"];
+type SourceKind = components["schemas"]["SourceKind"];
 
 interface FilterSidebarProps {
   rooms: Room[];

www/app/(app)/browse/_components/TranscriptCards.tsx

@@ -18,7 +18,10 @@ import {
   highlightMatches,
   generateTextFragment,
 } from "../../../lib/textHighlight";
-import { SearchResult, SourceKind } from "../../../lib/api-types";
+import type { components } from "../../../reflector-api";
+
+type SearchResult = components["schemas"]["SearchResult"];
+type SourceKind = components["schemas"]["SourceKind"];
 
 interface TranscriptCardsProps {
   results: SearchResult[];