Optimize home/library loading and SQLite query performance

- Replace home preview N+1 queries with a single window-function batch query
- Cache library previews and series card lists (15s TTL, shared with media cache)
- Tune SQLite: larger page cache, mmap, wal_autocheckpoint, ANALYZE on migrate
- Defer history fetch on library page until last_played sort is selected
- Yield to browser between paginated library loads to keep UI responsive

Co-authored-by: truewhile <truewhile@users.noreply.github.com>

internal/repository/media_repository_preview_test.go

@@ -0,0 +1,72 @@
+package repository
+
+import (
+	"fmt"
+	"testing"
+	"time"
+
+	"github.com/glebarez/sqlite"
+	"gorm.io/gorm"
+
+	"github.com/ShukeBta/MMTL/internal/database"
+	"github.com/ShukeBta/MMTL/internal/model"
+)
+
+func TestListRecentByLibraries(t *testing.T) {
+	db, err := gorm.Open(sqlite.Open(":memory:"), &gorm.Config{})
+	if err != nil {
+		t.Fatal(err)
+	}
+	if err := database.AutoMigrate(db); err != nil {
+		t.Fatalf("migrate: %v", err)
+	}
+	repos := New(db)
+
+	lib1 := model.Library{Name: "电影", Path: "/media/movies", Type: "movie", Enabled: true}
+	if err := repos.Library.Create(t.Context(), &lib1); err != nil {
+		t.Fatal(err)
+	}
+	lib2 := model.Library{Name: "动漫", Path: "/media/anime", Type: "anime", Enabled: true}
+	if err := repos.Library.Create(t.Context(), &lib2); err != nil {
+		t.Fatal(err)
+	}
+
+	now := time.Date(2026, 7, 2, 12, 0, 0, 0, time.UTC)
+	var rows []model.Media
+	for i := 1; i <= 5; i++ {
+		rows = append(rows, model.Media{
+			Base:      model.Base{ID: fmt.Sprintf("movie-%02d", i), CreatedAt: now.Add(time.Duration(i) * time.Hour)},
+			LibraryID: lib1.ID,
+			Title:     fmt.Sprintf("电影%d", i),
+			Path:      fmt.Sprintf("/media/movies/电影%d/movie%d.mp4", i, i),
+		})
+	}
+	for i := 1; i <= 8; i++ {
+		rows = append(rows, model.Media{
+			Base:       model.Base{ID: fmt.Sprintf("anime-ep-%02d", i), CreatedAt: now.Add(time.Duration(i) * time.Minute)},
+			LibraryID:  lib2.ID,
+			Title:      fmt.Sprintf("某动漫 第%d集", i),
+			Path:       fmt.Sprintf("/media/anime/某动漫/Season 01/某动漫.S01E%02d.mp4", i),
+			SeasonNum:  1,
+			EpisodeNum: i,
+		})
+	}
+	if err := repos.DB.Create(&rows).Error; err != nil {
+		t.Fatal(err)
+	}
+
+	filter := MediaQueryFilter{IncludeNSFW: true}
+	got, err := repos.Media.ListRecentByLibraries(t.Context(), []string{lib1.ID, lib2.ID}, 3, filter)
+	if err != nil {
+		t.Fatalf("ListRecentByLibraries failed: %v", err)
+	}
+	if len(got[lib1.ID]) != 3 {
+		t.Fatalf("lib1 recent count = %d, want 3", len(got[lib1.ID]))
+	}
+	if len(got[lib2.ID]) != 3 {
+		t.Fatalf("lib2 recent count = %d, want 3", len(got[lib2.ID]))
+	}
+	if got[lib1.ID][0].ID != "movie-05" {
+		t.Fatalf("lib1 newest = %q, want movie-05", got[lib1.ID][0].ID)
+	}
+}