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/_components/TranscriptCards.tsx

@@ -18,7 +18,7 @@ import {
   highlightMatches,
   generateTextFragment,
 } from "../../../lib/textHighlight";
-import { SearchResult } from "../../../lib/api-types";
+import { SearchResult, SourceKind } from "../../../lib/api-types";
 
 interface TranscriptCardsProps {
   results: SearchResult[];
@@ -120,7 +120,7 @@ function TranscriptCard({
     : "N/A";
   const formattedDate = formatLocalDate(result.created_at);
   const source =
-    result.source_kind === "room"
+    result.source_kind === ("room" as SourceKind)
       ? result.room_name || result.room_id
       : result.source_kind;