fix(worktrees): detect external merges, clean up empty dirs, prune in owning repo

- ContentInMain: HEAD ancestor of the default branch or squash-merged
  (merge-tree == target tree), against local origin/<default> without fetch;
  list_worktrees mergedIntoMain and the overview modal ("merged (external)")
  use it, "Cleanup finished" takes clean Active rows that are in main
- cleanup_task_worktree skips the dirty check for a non-git directory
- prune / worktree remove / branch -D run in the repo owning the worktree
  (git-common-dir), not the list's working dir; branch already gone reports
  branchDeleted=true

tests/ClaudeDo.Worker.Tests/External/WorktreeMcpToolsTests.cs

@@ -489,4 +489,45 @@ public sealed class WorktreeMcpToolsTests : IDisposable
             WorktreeMcpTools.ProgressReportInterval = original;
         }
     }
+
+    [Fact]
+    public async Task CleanupTaskWorktree_EmptyDirectory_RemovesDbRow()
+    {
+        if (!GitAvailable) { Assert.True(true, "git not available -- skipping"); return; }
+
+        var (task, list, wt) = await SeedWorktreeAsync(TaskStatus.Done);
+        // Leave an empty, non-git directory behind where the worktree was.
+        GitRepoFixture.RunGit(list.WorkingDir!, "worktree", "remove", "--force", wt.WorktreePath);
+        Directory.CreateDirectory(wt.WorktreePath);
+        var sut = BuildSut(CreateQueue());
+
+        var rows = await sut.ListWorktrees(CancellationToken.None);
+        Assert.Equal("", rows.Single(r => r.TaskId == task.Id).HeadCommit);
+
+        var result = await sut.CleanupTaskWorktree(task.Id, false, CancellationToken.None);
+
+        Assert.True(result.Removed);
+        Assert.False(Directory.Exists(wt.WorktreePath));
+        using var ctx = _db.CreateContext();
+        Assert.Null(await new WorktreeRepository(ctx).GetByTaskIdAsync(task.Id));
+    }
+
+    [Fact]
+    public async Task ListWorktrees_SquashMergedBranch_ReportsMergedIntoMain()
+    {
+        if (!GitAvailable) { Assert.True(true, "git not available -- skipping"); return; }
+
+        var (task, list, wt) = await SeedWorktreeAsync(TaskStatus.Done);
+        File.WriteAllText(Path.Combine(wt.WorktreePath, "feature.txt"), "x");
+        GitRepoFixture.RunGit(wt.WorktreePath, "add", "-A");
+        GitRepoFixture.RunGit(wt.WorktreePath, "commit", "-m", "feature");
+        GitRepoFixture.RunGit(list.WorkingDir!, "merge", "--squash", wt.BranchName);
+        GitRepoFixture.RunGit(list.WorkingDir!, "commit", "-m", "squash");
+        var sut = BuildSut(CreateQueue());
+
+        var row = (await sut.ListWorktrees(CancellationToken.None)).Single(r => r.TaskId == task.Id);
+
+        Assert.True(row.ContentInMain);
+        Assert.True(row.MergedIntoMain);
+    }
 }