Kept the app responsive while a backup copies the index (#1062)

app/MindWork AI Studio/Tools/Databases/AGENTS.md

@@ -24,6 +24,11 @@ When working on these, keep in mind:
 - **Let every probe in `GetDisplayInfo()` catch its own failure.** When the method throws, the page
   replaces the *entire* block with the fallback client, so one unreadable value costs all the others
   as well.
+- **SQLite runs its async methods synchronously.** `Microsoft.Data.Sqlite`, and EF Core on top of it,
+  only looks asynchronous: the calling thread does all the work. A statement which may take long, such
+  as `VACUUM` or a check of the whole database, runs in `Task.Run` inside the client, as
+  `BackupToDirectoryAsync` does. Otherwise a click in the user interface which reaches it freezes the
+  whole window until the statement is done.
 - **Raw SQL against SQLite goes through `context.Database.GetDbConnection()`**, not through
   `SqlQueryRaw<T>`: that one expects a column named `Value` and wraps the statement, so a `PRAGMA`
   never works with it.

app/MindWork AI Studio/Tools/Databases/IndexStore/SqliteIndexStoreClientImplementation.cs

@@ -590,9 +590,14 @@ public sealed partial class SqliteIndexStoreClientImplementation(string name, st
     /// GetDbConnection. The connections of the context share one cache, and a shared cache locks
     /// whole tables: reading the whole database for the copy would hold back every writer until the
     /// copy is done. Without pooling, nothing keeps the copy open afterward, so the backup can
-    /// delete it on every OS.
+    /// delete it on every OS.<br/><br/>
+    ///
+    /// SQLite runs its async methods synchronously, and copying and checking a large index takes a
+    /// while. The copy therefore runs on a thread of its own, so that it never holds up its caller.
     /// </remarks>
-    public override async Task<string> BackupToDirectoryAsync(string targetDirectory, CancellationToken token)
+    public override Task<string> BackupToDirectoryAsync(string targetDirectory, CancellationToken token) => Task.Run(() => this.CopyAndCheckAsync(targetDirectory, token), token);
+
+    private async Task<string> CopyAndCheckAsync(string targetDirectory, CancellationToken token)
     {
         Directory.CreateDirectory(targetDirectory);
         var targetPath = Path.Join(targetDirectory, DATABASE_FILENAME);