fix(home): keep finished series off the Continue-reading shelf

A "Continue reading" shelf listing series the reader already finished (read
to the last page, nothing new) is odd. Expose the last-read chapter's
page_count on the read-progress list, and filter the shelf to drop entries
that are caught up (on the last page of the latest chapter with no new
chapters). Mid-chapter and has-new-chapters entries stay; the full history
view is unaffected. Finished detection is a pure, unit-tested helper.

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

backend/tests/api_history.rs

@@ -191,6 +191,32 @@ async fn list_reports_new_chapters_since_last_read(pool: PgPool) {
     assert_eq!(body["items"][0]["new_chapters_count"], 2);
 }
 
+#[sqlx::test(migrations = "./migrations")]
+async fn list_reports_last_read_chapter_page_count(pool: PgPool) {
+    let h = common::harness(pool);
+    let (_, cookie) = common::register_user(&h.app).await;
+    let manga_id = common::seed_manga_via_api(&h.app, &cookie, "Berserk").await;
+    // seed_chapter uploads a single page, so page_count is 1.
+    let ch1 = seed_chapter(&h.app, &cookie, manga_id, 1).await;
+    let _ = upsert_progress(
+        &h.app,
+        &cookie,
+        json!({ "manga_id": manga_id.to_string(), "chapter_id": ch1, "page": 1 }),
+    )
+    .await;
+
+    let resp = h
+        .app
+        .clone()
+        .oneshot(common::get_with_cookie("/api/v1/me/read-progress", &cookie))
+        .await
+        .unwrap();
+    let body = common::body_json(resp).await;
+    // Exposes the last-read chapter's page count so a client can tell a
+    // finished series (on the last page) from one still in progress.
+    assert_eq!(body["items"][0]["chapter_page_count"], 1);
+}
+
 #[sqlx::test(migrations = "./migrations")]
 async fn list_new_chapters_count_is_zero_at_latest_chapter(pool: PgPool) {
     let h = common::harness(pool);