feat: pg_trgm search, sort options, populated total count

Backend:
- Migration 0005_search.sql enables pg_trgm and adds GIN indexes
  (gin_trgm_ops) on mangas.title and on mangas.author (partial, WHERE
  author IS NOT NULL).
- repo::manga::list keeps the existing substring (ILIKE) clause and
  adds the `%` operator on title + author so the search tolerates typos
  ('narto' → 'Naruto'). Both branches share the trgm index. A second
  count(*) query (same WHERE clause, indexed) yields the total without
  scanning twice in any meaningful sense.
- New ListSort enum (Recent / Title) interpolated into ORDER BY from a
  hard-coded match — never from request input, so the format!() is not
  a SQL-injection seam. Default stays Recent (created_at DESC).
- api::mangas accepts `?sort=recent|title` (snake_case) via serde and
  returns `page.total` as a number instead of null.
- api::pagination::PagedResponse gains a `with_total` constructor.

Backend coverage in tests/api_mangas.rs (4 new cases plus the existing
list_is_empty_initially updated to assert total: 0):
- list_returns_total_count_independent_of_pagination — limit=2 with 3
  rows returns 2 items and total=3.
- search_via_trigram_tolerates_typos — `?search=narto` finds Naruto.
- list_sort_title_orders_alphabetically — three out-of-order inserts
  come back A→Z.
- search_reflects_filtered_total — search narrows total to 1.

Frontend:
- lib/api/mangas.ts gains a `MangaSort` type and threads `sort` through
  listMangas's query-string builder.
- Home page renders a "Sort" select (Recent / Title A→Z) that re-runs
  the list query, and shows "Showing N of M" when total is present.

Lockstep version bump to 0.8.0.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

backend/tests/api_mangas.rs

@@ -20,7 +20,130 @@ async fn list_is_empty_initially(pool: PgPool) {
     assert_eq!(body["items"], json!([]));
     assert_eq!(body["page"]["limit"], 50);
     assert_eq!(body["page"]["offset"], 0);
-    assert!(body["page"]["total"].is_null());
+    assert_eq!(body["page"]["total"], 0);
+}
+
+#[sqlx::test(migrations = "./migrations")]
+async fn list_returns_total_count_independent_of_pagination(pool: PgPool) {
+    let h = common::harness(pool);
+    let (_, cookie) = common::register_user(&h.app).await;
+
+    for title in ["One Piece", "Berserk", "Vinland Saga"] {
+        let _ = h
+            .app
+            .clone()
+            .oneshot(common::post_multipart_with_cookie(
+                "/api/v1/mangas",
+                MultipartBuilder::new().add_json("metadata", json!({ "title": title })),
+                &cookie,
+            ))
+            .await
+            .unwrap();
+    }
+
+    let resp = h
+        .app
+        .oneshot(common::get("/api/v1/mangas?limit=2"))
+        .await
+        .unwrap();
+    let body = common::body_json(resp).await;
+    assert_eq!(body["items"].as_array().unwrap().len(), 2);
+    // Total reflects the unfiltered population, not the page size.
+    assert_eq!(body["page"]["total"], 3);
+}
+
+#[sqlx::test(migrations = "./migrations")]
+async fn search_via_trigram_tolerates_typos(pool: PgPool) {
+    let h = common::harness(pool);
+    let (_, cookie) = common::register_user(&h.app).await;
+    let _ = h
+        .app
+        .clone()
+        .oneshot(common::post_multipart_with_cookie(
+            "/api/v1/mangas",
+            MultipartBuilder::new().add_json("metadata", json!({ "title": "Naruto" })),
+            &cookie,
+        ))
+        .await
+        .unwrap();
+
+    // 'narto' is one letter off — the % operator on the GIN trgm index
+    // should still match it.
+    let resp = h
+        .app
+        .oneshot(common::get("/api/v1/mangas?search=narto"))
+        .await
+        .unwrap();
+    let body = common::body_json(resp).await;
+    let titles: Vec<&str> = body["items"]
+        .as_array()
+        .unwrap()
+        .iter()
+        .map(|m| m["title"].as_str().unwrap())
+        .collect();
+    assert_eq!(titles, vec!["Naruto"]);
+    assert_eq!(body["page"]["total"], 1);
+}
+
+#[sqlx::test(migrations = "./migrations")]
+async fn list_sort_title_orders_alphabetically(pool: PgPool) {
+    let h = common::harness(pool);
+    let (_, cookie) = common::register_user(&h.app).await;
+
+    for title in ["Vinland Saga", "Berserk", "One Piece"] {
+        let _ = h
+            .app
+            .clone()
+            .oneshot(common::post_multipart_with_cookie(
+                "/api/v1/mangas",
+                MultipartBuilder::new().add_json("metadata", json!({ "title": title })),
+                &cookie,
+            ))
+            .await
+            .unwrap();
+    }
+
+    let resp = h
+        .app
+        .oneshot(common::get("/api/v1/mangas?sort=title"))
+        .await
+        .unwrap();
+    let body = common::body_json(resp).await;
+    let titles: Vec<&str> = body["items"]
+        .as_array()
+        .unwrap()
+        .iter()
+        .map(|m| m["title"].as_str().unwrap())
+        .collect();
+    assert_eq!(titles, vec!["Berserk", "One Piece", "Vinland Saga"]);
+}
+
+#[sqlx::test(migrations = "./migrations")]
+async fn search_reflects_filtered_total(pool: PgPool) {
+    let h = common::harness(pool);
+    let (_, cookie) = common::register_user(&h.app).await;
+
+    for title in ["One Piece", "Berserk", "Vinland Saga"] {
+        let _ = h
+            .app
+            .clone()
+            .oneshot(common::post_multipart_with_cookie(
+                "/api/v1/mangas",
+                MultipartBuilder::new().add_json("metadata", json!({ "title": title })),
+                &cookie,
+            ))
+            .await
+            .unwrap();
+    }
+
+    let resp = h
+        .app
+        .oneshot(common::get("/api/v1/mangas?search=berserk"))
+        .await
+        .unwrap();
+    let body = common::body_json(resp).await;
+    assert_eq!(body["items"].as_array().unwrap().len(), 1);
+    assert_eq!(body["page"]["total"], 1);
 }
 
 #[sqlx::test(migrations = "./migrations")]