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] {

src/versions/mod.rs

@@ -363,25 +363,34 @@ pub fn link_pending(
 /// responses stay byte-identical for libraries that have none.
 ///
 /// `display_path` is `null` when the original is displayed, a rel_path when a
-/// version is. `/photos` carries the same facts as the parallel arrays
-/// `photo_display_paths` / `photo_version_counts` instead.
+/// version is. `clip_count` counts derived clips (videos made from the
+/// photo), which are not versions. `/photos` carries the same facts as the
+/// parallel arrays `photo_display_paths` / `photo_version_counts` /
+/// `photo_clip_counts` instead.
 #[derive(Debug, Clone, Default, serde::Serialize)]
 pub struct VersionFields {
     #[serde(skip_serializing_if = "Option::is_none")]
     pub display_path: Option<Option<String>>,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub version_count: Option<u32>,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub clip_count: Option<u32>,
 }
 
 impl VersionFields {
     pub fn from_summary(summary: Option<&version_dao::PhotoVersionSummary>) -> Self {
-        match summary {
-            Some(s) if s.version_count > 0 => VersionFields {
-                display_path: Some(s.display.as_ref().map(|(_, p)| p.clone())),
-                version_count: Some(s.version_count),
-            },
-            _ => VersionFields::default(),
+        let Some(s) = summary else {
+            return VersionFields::default();
+        };
+        let mut fields = VersionFields::default();
+        if s.version_count > 0 {
+            fields.display_path = Some(s.display.as_ref().map(|(_, p)| p.clone()));
+            fields.version_count = Some(s.version_count);
         }
+        if s.clip_count > 0 {
+            fields.clip_count = Some(s.clip_count);
+        }
+        fields
     }
 }
 
@@ -451,6 +460,7 @@ mod tests {
         assert_eq!(json(None), serde_json::json!({"path": "a.jpg"}));
         let plain = version_dao::PhotoVersionSummary {
             version_count: 2,
+            clip_count: 0,
             display: None,
         };
         assert_eq!(
@@ -459,6 +469,7 @@ mod tests {
         );
         let shown = version_dao::PhotoVersionSummary {
             version_count: 1,
+            clip_count: 0,
             display: Some((1, "aiedits/a.jpg.restored.png".into())),
         };
         assert_eq!(
@@ -469,6 +480,16 @@ mod tests {
                 "version_count": 1
             })
         );
+        // Clips only: no display/version fields, just the clip count.
+        let clips_only = version_dao::PhotoVersionSummary {
+            version_count: 0,
+            clip_count: 2,
+            display: None,
+        };
+        assert_eq!(
+            json(Some(&clips_only)),
+            serde_json::json!({"path": "a.jpg", "clip_count": 2})
+        );
     }
 
     #[test]