feat: complete migration from @hey-api/openapi-ts to openapi-react-query

- Migrated all components from useApi compatibility layer to direct React Query hooks
- Added new hooks for participant operations, room meetings, and speaker operations
- Updated all imports from old api module to api-types
- Fixed TypeScript types and API endpoint signatures
- Removed deprecated useApi.ts compatibility layer
- Fixed SourceKind enum values to match OpenAPI spec
- Added @ts-ignore for Zulip endpoints not in OpenAPI spec yet
- Fixed all compilation errors and type issues

www/app/(app)/browse/page.tsx

@@ -204,7 +204,7 @@ export default function TranscriptBrowser() {
 
   const [urlSourceKind, setUrlSourceKind] = useQueryState(
     "source",
-    parseAsStringLiteral($SourceKind.enum).withOptions({
+    parseAsStringLiteral($SourceKind.values).withOptions({
       shallow: false,
     }),
   );
@@ -302,7 +302,6 @@ export default function TranscriptBrowser() {
         params: {
           path: { transcript_id: transcriptId },
         },
-        body: {},
       },
       {
         onSuccess: (result) => {