refactor(web): migrate playlists.ts to api.* wrapper (#375)

Drop 9 hand-rolled apiFetch calls with redundant Content-Type
headers + manual JSON.stringify. The api.* wrapper in client.ts
already handles both. Identical wire shape; existing tests cover
all endpoints.

Also makes api.del generic so DELETE endpoints with typed returns
(playlist track removal) can use the wrapper instead of raw
apiFetch. Default `T = null` preserves existing callers.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

web/src/lib/api/client.ts

@@ -58,6 +58,6 @@ export const api = {
     apiFetch(path, { method: 'PUT', body: JSON.stringify(body) }) as Promise<T>,
   patch: <T>(path: string, body: unknown): Promise<T> =>
     apiFetch(path, { method: 'PATCH', body: JSON.stringify(body) }) as Promise<T>,
-  del: (path: string): Promise<null> =>
-    apiFetch(path, { method: 'DELETE' }) as Promise<null>
+  del: <T = null>(path: string): Promise<T> =>
+    apiFetch(path, { method: 'DELETE' }) as Promise<T>
 };