fix(polecat): ignore .beads/ files when detecting uncommitted work

Add CleanExcludingBeads() method that returns true if the only uncommitted
changes are .beads/ database files. These files are synced across worktrees
and shouldn't block polecat cleanup.

Fixes #516

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/git/git.go

@@ -973,6 +973,37 @@ func (s *UncommittedWorkStatus) Clean() bool {
 	return !s.HasUncommittedChanges && s.StashCount == 0 && s.UnpushedCommits == 0
 }
 
+// CleanExcludingBeads returns true if the only uncommitted changes are .beads/ files.
+// This is useful for polecat stale detection where beads database files are synced
+// across worktrees and shouldn't block cleanup.
+func (s *UncommittedWorkStatus) CleanExcludingBeads() bool {
+	// Stashes and unpushed commits always count as uncommitted work
+	if s.StashCount > 0 || s.UnpushedCommits > 0 {
+		return false
+	}
+
+	// Check if all modified files are beads files
+	for _, f := range s.ModifiedFiles {
+		if !isBeadsPath(f) {
+			return false
+		}
+	}
+
+	// Check if all untracked files are beads files
+	for _, f := range s.UntrackedFiles {
+		if !isBeadsPath(f) {
+			return false
+		}
+	}
+
+	return true
+}
+
+// isBeadsPath returns true if the path is a .beads/ file.
+func isBeadsPath(path string) bool {
+	return strings.Contains(path, ".beads/") || strings.Contains(path, ".beads\\")
+}
+
 // String returns a human-readable summary of uncommitted work.
 func (s *UncommittedWorkStatus) String() string {
 	var issues []string

internal/polecat/manager.go

@@ -1021,9 +1021,9 @@ func (m *Manager) DetectStalePolecats(threshold int) ([]*StalenessInfo, error) {
 		polecatGit := git.NewGit(p.ClonePath)
 		info.CommitsBehind = countCommitsBehind(polecatGit, defaultBranch)
 
-		// Check for uncommitted work
+		// Check for uncommitted work (excluding .beads/ files which are synced across worktrees)
 		status, err := polecatGit.CheckUncommittedWork()
-		if err == nil && !status.Clean() {
+		if err == nil && !status.CleanExcludingBeads() {
 			info.HasUncommittedWork = true
 		}