gelbooru: re-add background prefetch for batch API fast path only

When _batch_api_works is True (Gelbooru proper with auth, persisted
from a prior session's probe), search() fires prefetch_batch in the
background. The batch tag API covers the entire page's tags in 1-2
requests during the time between grid render and user click — the
cache is warm before the info panel opens, so categories appear
instantly with no flash of flat tags.

Gated on _batch_api_works is True (not None, not False):
  - Gelbooru proper: prefetches (batch API known good)
  - Rule34: skips (batch_api_works = False, persisted)
  - Safebooru.org: skips (no auth → fetcher skips batch capability)

Rule34 / Safebooru.org / Moebooru stay on-demand: the ~200ms
per-click HTML scrape is unavoidable for those sites because their
only path is per-post page fetching, which can't be batched.

booru_viewer/core/api/gelbooru.py

@@ -81,6 +81,18 @@ class GelbooruClient(BooruClient):
                     created_at=_parse_date(item.get("created_at")),
                 )
             )
+        # Background prefetch ONLY when the batch tag API is known to
+        # work (persisted probe result = True, i.e. Gelbooru proper
+        # with auth). One request covers all tags for the page, so the
+        # cache is warm before the user clicks. Rule34/Safebooru.org
+        # skip this (batch_api_works is False or None) — their only
+        # path is per-post HTML which runs on click.
+        if (
+            self.category_fetcher is not None
+            and self.category_fetcher._batch_api_works is True
+        ):
+            import asyncio
+            asyncio.create_task(self.category_fetcher.prefetch_batch(posts))
         return posts
 
     @staticmethod