fix(sync): prevent final flush after sync.branch restore

When sync.branch is configured, the sync command:
1. Exports changes to JSONL
2. Commits to sync branch via worktree
3. Pulls from sync branch
4. Restores .beads/ from HEAD to keep working directory clean

But PersistentPostRun's flushManager.Shutdown() was re-exporting to JSONL,
undoing the restore and leaving modified files.

Fix: Set skipFinalFlush flag when sync.branch mode completes successfully.
This prevents the final export in PersistentPostRun.

Also: Skip push to main branch when sync.branch is configured - all
pushes should go through the sync branch worktree.

cmd/bd/main.go

@@ -82,6 +82,10 @@ var (
 	// Auto-flush manager (replaces timer-based approach to fix bd-52)
 	flushManager *FlushManager
 
+	// skipFinalFlush is set by sync command when sync.branch mode completes successfully.
+	// This prevents PersistentPostRun from re-exporting and dirtying the working directory.
+	skipFinalFlush = false
+
 	// Auto-import state
 	autoImportEnabled = true // Can be disabled with --no-auto-import
 
@@ -613,7 +617,8 @@ var rootCmd = &cobra.Command{
 
 		// Otherwise, handle direct mode cleanup
 		// Shutdown flush manager (performs final flush if needed)
-		if flushManager != nil {
+		// Skip if sync command already handled export and restore (sync.branch mode)
+		if flushManager != nil && !skipFinalFlush {
 			if err := flushManager.Shutdown(); err != nil {
 				fmt.Fprintf(os.Stderr, "Warning: flush manager shutdown error: %v\n", err)
 			}

cmd/bd/sync.go

@@ -577,8 +577,10 @@ Use --merge to merge the sync branch back to main branch.`,
 			}
 		}
 
-		// Step 5: Push to remote (skip if already pushed via sync branch worktree)
-		if !noPush && hasChanges && !pushedViaSyncBranch {
+		// Step 5: Push to remote (skip if using sync branch - all pushes go via worktree)
+		// When sync.branch is configured, we don't push the main branch at all.
+		// The sync branch worktree handles all pushes.
+		if !noPush && hasChanges && !pushedViaSyncBranch && !useSyncBranch {
 			if dryRun {
 				fmt.Println("→ [DRY RUN] Would push to remote")
 			} else {
@@ -616,6 +618,9 @@ Use --merge to merge the sync branch back to main branch.`,
 					// Non-fatal - just means git status will show modified files
 					debug.Logf("sync: failed to restore .beads/ from branch: %v", err)
 				}
+				// Skip final flush in PersistentPostRun - we've already exported to sync branch
+				// and restored the working directory to match the current branch
+				skipFinalFlush = true
 			}
 
 			fmt.Println("\n✓ Sync complete")