perf: precompute mangas.sort_author for the author sort

?sort=author used a correlated min(lower(a.name)) subquery as the ORDER BY
key, evaluated per filter-matching row before LIMIT. Materialize it into
mangas.sort_author (indexed by mangas_sort_author_idx), maintained by triggers
on manga_authors and backfilled in the migration, so the sort is a plain
indexed column read. Author names are immutable, so only join changes matter.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/tests/api_mangas_metadata.rs

@@ -326,6 +326,54 @@ async fn patch_updates_status_authors_and_genres(pool: PgPool) {
     assert_eq!(body["genres"][0]["name"], "Drama");
 }
 
+#[sqlx::test(migrations = "./migrations")]
+async fn patch_authors_updates_precomputed_sort_author(pool: PgPool) {
+    // The precomputed mangas.sort_author (used by ?sort=author) must track
+    // author edits: changing the alphabetically-first author reorders the
+    // author sort. Two mangas whose relative author order flips after a PATCH.
+    let h = common::harness(pool.clone());
+    let (_, cookie) = common::register_user(&h.app).await;
+
+    let a = id_of(&create_manga(&h.app, &cookie, json!({ "title": "A", "authors": ["Zeta"] })).await);
+    let _b = id_of(&create_manga(&h.app, &cookie, json!({ "title": "B", "authors": ["Mid"] })).await);
+
+    // Initially: Mid < Zeta, so B before A.
+    let ids = list_titles(&h.app, "sort=author&order=asc").await;
+    assert_eq!(ids, vec!["B", "A"]);
+
+    // Re-author A to "Alpha", which now sorts first.
+    let resp = h
+        .app
+        .clone()
+        .oneshot(common::patch_json_with_cookie(
+            &format!("/api/v1/mangas/{a}"),
+            json!({ "authors": ["Alpha"] }),
+            &cookie,
+        ))
+        .await
+        .unwrap();
+    assert_eq!(resp.status(), StatusCode::OK);
+
+    // Now A (Alpha) sorts before B (Mid) — proving sort_author was recomputed.
+    let ids = list_titles(&h.app, "sort=author&order=asc").await;
+    assert_eq!(ids, vec!["A", "B"]);
+}
+
+async fn list_titles(app: &axum::Router, query: &str) -> Vec<String> {
+    let resp = app
+        .clone()
+        .oneshot(common::get(&format!("/api/v1/mangas?{query}")))
+        .await
+        .unwrap();
+    let body = common::body_json(resp).await;
+    body["items"]
+        .as_array()
+        .unwrap()
+        .iter()
+        .map(|m| m["title"].as_str().unwrap().to_string())
+        .collect()
+}
+
 #[sqlx::test(migrations = "./migrations")]
 async fn patch_404_on_unknown_id(pool: PgPool) {
     let h = common::harness(pool);