Extract a per-user background host so indexing can later run outside the window.

Keep the GUI as the index writer for now; mutex, named pipe, and opt-in logon autostart prepare Explorer.Host.exe without two SQLite writers.

Co-authored-by: Cursor <cursoragent@cursor.com>

tests/Explorer.Storage.Tests/StorageTests.cs

@@ -427,3 +427,28 @@ public class FileRelationTests
         Assert.Empty(await store.OperationProfiles.ListAsync());
     }
 }
+
+public class IndexStoreLockTests
+{
+    [Fact]
+    public async Task Second_writer_on_same_path_is_rejected()
+    {
+        var path = Path.Combine(Path.GetTempPath(), "ew-tests", Guid.NewGuid().ToString("N"), "index.db");
+        await using var first = new SqliteIndexStore(path, NullLogger<SqliteIndexStore>.Instance);
+        await first.OpenAsync();
+        var second = new SqliteIndexStore(path, NullLogger<SqliteIndexStore>.Instance);
+        var ex = await Assert.ThrowsAsync<InvalidOperationException>(() => second.OpenAsync());
+        Assert.Contains("already in use", ex.Message, StringComparison.OrdinalIgnoreCase);
+        await first.DisposeAsync();
+        await second.OpenAsync();
+        await second.DisposeAsync();
+    }
+
+    [Fact]
+    public void Mutex_name_is_stable_for_the_same_path()
+    {
+        var path = @"C:\Users\me\AppData\Local\ExplorerWorkbench\index.db";
+        Assert.Equal(IndexStoreLock.MutexNameFor(path), IndexStoreLock.MutexNameFor(path));
+        Assert.StartsWith(@"Local\ExplorerWorkbench-Index-", IndexStoreLock.MutexNameFor(path));
+    }
+}