Clip counts on listings, so clients find photos with only clips

Derived clips (#208) aren't counted as versions, so a photo whose only
derived file is a clip looked like a plain photo, and clients never fetched
/image/versions for it. Summaries now carry clip_count: /photos adds the
parallel array photo_clip_counts, records (memories, search, /photos/exif)
carry clip_count. All skipped when zero, so other responses are unchanged.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/versions/integration_tests.rs

@@ -798,10 +798,12 @@ async fn an_animated_clip_links_hides_and_is_listed_apart_from_versions() {
     );
     let app = photos_app!(fx);
 
-    // Hidden behind the photo, like a version, and not counted as one.
+    // Hidden behind the photo, like a version, and counted as a clip, not a
+    // version (so the viewer knows to fetch /image/versions for it).
     let (_, body) = get_json!(app, "/photos?path=&recursive=true&sort=nameasc");
     assert_eq!(body["photos"], serde_json::json!(["2014/IMG_1.JPG"]));
     assert!(body.get("photo_version_counts").is_none(), "{body}");
+    assert_eq!(body["photo_clip_counts"], serde_json::json!([1]));
 
     // Listed under `clips`, from the photo's path or the clip's own.
     for path in ["2014/IMG_1.JPG", rel] {