feat(catalog): Latest Episodes sort — order series by newest episode file (#283)

* feat(catalog): Latest Episodes sort — order series by newest episode file

Adds a latest_episode_added sort so users can see which shows received
new episodes. Today's recently-added surfaces reflect when the SERIES
was first added: linking a new episode file never bumps the series'
media_item_libraries.first_seen_at (ON CONFLICT DO NOTHING), so a
long-running show with a fresh episode sorts as stale (#202).

- New denorm media_items.latest_episode_added_at (migration + backfill
  + partial series index), mirroring the last_air_date_at precedent.
  Source of truth is episode_libraries.first_seen_at; the three insert
  paths (UpdateEpisodeLink, BulkLinkEpisodesBySeries, scanner folder
  restore) bump the parent series atomically in the same statement,
  monotonically via GREATEST, and only for genuinely new links.
- Sort registered in both frameworks: querySortDefs (sections + smart
  collections + /v1/catalog pick it up automatically via
  QuerySortFieldSet) and the browse buildOrderByPlan path.
- Jellyfin compat: SortBy=DateLastContentAdded now maps to the new sort
  instead of silently collapsing to series creation date — Jellyfin
  clients already send this for the TV "Latest" shelf, so they get the
  correct behavior with no client changes. DatePlayed keeps its old
  created_at mapping instead of piggybacking.
- Web sort picker gains "Latest Episode Added" (series scope).

Additive-only per v1 API rules: new sort value, no field/status changes.

Part of #202
Fixes #202

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

* fix(web): include latest_episode_added in the api QuerySort field union

The picker-side QuerySortField gained the value but the api-layer
QuerySort union did not, breaking the production tsc build.

Part of #202

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

* fix(scanner): recompute latest_episode_added_at when episode memberships are removed

The denorm was only ever bumped upward (GREATEST) at insert time, but
UpdateEpisodeLink also deletes the old episode's library membership on
re-link, and reconciliation/path-prefix clears remove memberships too —
leaving a stale timestamp that kept the series sorting as recently
updated. All removal paths now run in a transaction and finish with a
shared full MAX() recompute (catalog.RecomputeSeriesLatestEpisodeAdded)
that also resets to NULL when no memberships remain, mirroring the
last_air_date_at maintenance pattern.

Sequential statements are load-bearing here: data-modifying CTEs are
invisible to reads in the same statement, which also silently no-op'd
the old path-prefix membership delete.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

* fix(jellycompat): keep DateLastContentAdded scoped to series-only requests

mapSortBy runs for every /Items browse, so the latest_episode_added
mapping leaked into movie and untyped requests where the column is
always NULL, destroying the previous created_at ordering. The sort now
falls back to created_at unless IncludeItemTypes is exactly Series.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

---------

Co-authored-by: Claude Fable 5 <noreply@anthropic.com>
Co-authored-by: Quick <31828688+Quick104@users.noreply.github.com>

web/src/api/types.ts

@@ -1343,6 +1343,7 @@ export interface QuerySort {
     | "added_at"
     | "release_date"
     | "last_air_date"
+    | "latest_episode_added"
     | "year"
     | "content_rating"
     | "runtime"