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>

CLAUDE.md

@@ -364,7 +364,8 @@ to the original, as `<dir>/aiedits/<original name>.<kind>[.<n>].png`. A
 **derived clip** (kind `animated`, `CLIP_KINDS`) is a video made from a photo
 (Enhance "Animate", `<name>.animated[.<n>].mp4`): linked, hidden and lifecycled
 exactly like a version, but never counted as one (`photo_version_counts`,
-`version_count`), never a display choice (`PUT /image/versions/display` answers 400
+`version_count`; they have their own `photo_clip_counts` / `clip_count`, so clients
+know to fetch `/image/versions` for a photo with only clips), never a display choice (`PUT /image/versions/display` answers 400
 `clip_not_displayable`), and listed apart, as `clips` in `GET /image/versions`. ImageApi
 only detects it (library roots stay read-only) and shows original + versions as
 **one photo**; a *global* choice (not per user) says which file is displayed.
@@ -751,8 +752,9 @@ GET /image/versions?path=...&library=...   (path of the original or any version
 POST /enhance ...                          (Enhance on demand; see "Enhance on demand")
 PUT /image/versions/display                (body { path, display_hash|null, library? }; global choice)
 //   /photos hides versions behind their original (include_versions=true lists them) and adds
-//   parallel arrays photo_display_paths / photo_version_counts; memories items, search hits and
-//   /photos/exif rows carry display_path / version_count. All skipped when there are none.
+//   parallel arrays photo_display_paths / photo_version_counts / photo_clip_counts; memories items,
+//   search hits and /photos/exif rows carry display_path / version_count / clip_count. All skipped
+//   when there are none.
 
 // Memories (week-based grouping)
 GET /memories?path=...&recursive=true