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)/transcripts/shareZulip.tsx

@@ -1,6 +1,9 @@
 import { useState, useEffect, useMemo } from "react";
 import { featureEnabled } from "../../domainContext";
-import { GetTranscript, GetTranscriptTopic } from "../../lib/api-types";
+import type { components } from "../../reflector-api";
+
+type GetTranscript = components["schemas"]["GetTranscript"];
+type GetTranscriptTopic = components["schemas"]["GetTranscriptTopic"];
 import {
   BoxProps,
   Button,