Perform download cache renewal async

Don't block on cache renewals, but notify library on updates so that the badges show up when ready.

We skip the cache when checking if a chapter is downloaded for the reader assuming that it's a
relatively low cost to check for a single chapter.

(Probably) fixes #8254 / fixes #7847

app/src/main/java/eu/kanade/tachiyomi/ui/library/LibraryPresenter.kt

@@ -39,6 +39,7 @@ import eu.kanade.presentation.library.components.LibraryToolbarTitle
 import eu.kanade.tachiyomi.R
 import eu.kanade.tachiyomi.data.cache.CoverCache
 import eu.kanade.tachiyomi.data.database.models.toDomainManga
+import eu.kanade.tachiyomi.data.download.DownloadCache
 import eu.kanade.tachiyomi.data.download.DownloadManager
 import eu.kanade.tachiyomi.data.track.TrackManager
 import eu.kanade.tachiyomi.source.SourceManager
@@ -88,6 +89,7 @@ class LibraryPresenter(
     private val coverCache: CoverCache = Injekt.get(),
     private val sourceManager: SourceManager = Injekt.get(),
     private val downloadManager: DownloadManager = Injekt.get(),
+    private val downloadCache: DownloadCache = Injekt.get(),
     private val trackManager: TrackManager = Injekt.get(),
 ) : BasePresenter<LibraryController>(), LibraryState by state {
 
@@ -338,7 +340,8 @@ class LibraryPresenter(
         val libraryMangasFlow = combine(
             getLibraryManga.subscribe(),
             libraryPreferences.downloadBadge().changes(),
-        ) { libraryMangaList, downloadBadgePref ->
+            downloadCache.changes,
+        ) { libraryMangaList, downloadBadgePref, _ ->
             libraryMangaList
                 .map { libraryManga ->
                     // Display mode based on user preference: take it from global library setting or category