feat(api): admin manga/chapter overview with derived sync state (0.39.0)

Adds GET /api/v1/admin/mangas and /admin/mangas/:id/chapters guarded by
RequireAdmin. Sync state is computed at query time from the existing
crawler signals (manga_sources / chapter_sources / crawler_jobs) — no
new state column is persisted, so the crawler stays the single writer
of these signals.

Per-manga priority: InProgress (in-flight sync_manga or
sync_chapter_list job) > Dropped (all source rows soft-dropped) >
Synced (default; covers user-uploaded mangas with zero source rows).

Per-chapter priority: Downloading (in-flight sync_chapter_content) >
Dropped (all source rows soft-dropped) > Failed (most-recent terminal
job is dead) > NotDownloaded (page_count = 0) > Synced. The Failed
check sits ABOVE NotDownloaded so the more informative "we tried and
it died" state wins over "we never got around to it" — see the
priority comment in repo/admin_view.rs.

Migration 0020 adds a partial index on
crawler_jobs((payload->>'source_manga_key')) for the one job kind
(sync_manga) whose payload doesn't carry manga_id directly — without it
the in-flight detection for a manga falls back to a seqscan over the
job table.

backend/src/domain/sync_state.rs

@@ -0,0 +1,46 @@
+//! Sync-state enums derived per-manga / per-chapter from `manga_sources`,
+//! `chapter_sources`, and `crawler_jobs` at query time. No state column
+//! is persisted on `mangas` / `chapters` — see `repo::admin_view` for the
+//! derivation rules and priority order.
+
+use serde::{Deserialize, Serialize};
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize, sqlx::Type)]
+#[sqlx(type_name = "text", rename_all = "snake_case")]
+#[serde(rename_all = "snake_case")]
+pub enum MangaSyncState {
+    /// A `sync_manga` or `sync_chapter_list` job is currently
+    /// pending or running for this manga.
+    InProgress,
+    /// At least one `manga_sources` row exists for this manga and ALL of
+    /// them have `dropped_at IS NOT NULL` — every source we know about
+    /// has stopped surfacing it.
+    Dropped,
+    /// Default healthy state: at least one live source row OR the manga
+    /// was user-uploaded (no `manga_sources` rows at all).
+    Synced,
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize, sqlx::Type)]
+#[sqlx(type_name = "text", rename_all = "snake_case")]
+#[serde(rename_all = "snake_case")]
+pub enum ChapterSyncState {
+    /// A `sync_chapter_content` job is currently pending or running for
+    /// this chapter (the 0014 dedup index guarantees at most one).
+    Downloading,
+    /// At least one `chapter_sources` row exists AND all of them are
+    /// `dropped_at IS NOT NULL`.
+    Dropped,
+    /// Most recent `sync_chapter_content` job for this chapter is `dead`
+    /// (terminal failure). Checked BEFORE `NotDownloaded` so the more
+    /// informative "we tried and it died" state wins over "we never
+    /// got around to it".
+    Failed,
+    /// `page_count = 0` and no in-flight or failed job — the chapter
+    /// row exists but content has never been downloaded.
+    NotDownloaded,
+    /// `page_count > 0` — content has been downloaded at some point.
+    /// Reaped `done` jobs in `crawler_jobs` mean we can't read this from
+    /// the job table, so `page_count` is the durable truth.
+    Synced,
+}