chore(gastown): scorched-earth SQLite removal from codebase

Remove all bd sync references and SQLite-specific code from gastown:

**Formulas (agent priming):**
- mol-polecat-work: Remove bd sync step from prepare-for-review
- mol-sync-workspace: Replace sync-beads step with verify-beads (Dolt check)
- mol-polecat-conflict-resolve: Remove bd sync from close-beads
- mol-polecat-code-review: Remove bd sync from summarize-review and complete-and-exit
- mol-polecat-review-pr: Remove bd sync from complete-and-exit
- mol-convoy-cleanup: Remove bd sync from archive-convoy
- mol-digest-generate: Remove bd sync from send-digest
- mol-town-shutdown: Replace sync-state step with verify-state
- beads-release: Replace restart-daemons with verify-install (no daemons with Dolt)

**Templates (role priming):**
- mayor.md.tmpl: Update session end checklist to remove bd sync steps
- crew.md.tmpl: Remove bd sync references from workflow and checklist
- polecat.md.tmpl: Update self-cleaning model and session close docs
- spawn.md.tmpl: Remove bd sync from completion steps
- nudge.md.tmpl: Remove bd sync from completion steps

**Go code:**
- session_manager.go: Remove syncBeads function and call
- rig_dock.go: Remove bd sync calls from dock/undock
- crew/manager.go: Remove runBdSync, update Pristine function
- crew_maintenance.go: Remove bd sync status output
- crew.go: Update pristine command help text
- polecat.go: Make sync command a no-op with deprecation message
- daemon/lifecycle.go: Remove bd sync from startup sequence
- doctor/beads_check.go: Update fix hints and Fix to use bd import not bd sync
- doctor/rig_check.go: Remove sync status check, simplify BeadsConfigValidCheck
- beads/beads.go: Update primeContent to remove bd sync references

With Dolt backend, beads changes are persisted immediately to the sql-server.
There is no separate sync step needed.

Part of epic: hq-e4eefc (SQLite removal)

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

internal/cmd/polecat.go

@@ -110,11 +110,11 @@ Examples:
 
 var polecatSyncCmd = &cobra.Command{
 	Use:   "sync <rig>/<polecat>",
-	Short: "Sync beads for a polecat",
+	Short: "Sync beads for a polecat (deprecated with Dolt backend)",
 	Long: `Sync beads for a polecat's worktree.
 
-Runs 'bd sync' in the polecat's worktree to push local beads changes
-to the shared sync branch and pull remote changes.
+NOTE: With Dolt backend, beads changes are persisted immediately.
+This command is a no-op when using Dolt.
 
 Use --all to sync all polecats in a rig.
 Use --from-main to only pull (no push).
@@ -534,87 +534,9 @@ func runPolecatRemove(cmd *cobra.Command, args []string) error {
 }
 
 func runPolecatSync(cmd *cobra.Command, args []string) error {
-	if len(args) < 1 {
-		return fmt.Errorf("rig or rig/polecat address required")
-	}
-
-	// Parse address - could be "rig" or "rig/polecat"
-	rigName, polecatName, err := parseAddress(args[0])
-	if err != nil {
-		// Might just be a rig name
-		rigName = args[0]
-		polecatName = ""
-	}
-
-	mgr, _, err := getPolecatManager(rigName)
-	if err != nil {
-		return err
-	}
-
-	// Get list of polecats to sync
-	var polecatsToSync []string
-	if polecatSyncAll || polecatName == "" {
-		polecats, err := mgr.List()
-		if err != nil {
-			return fmt.Errorf("listing polecats: %w", err)
-		}
-		for _, p := range polecats {
-			polecatsToSync = append(polecatsToSync, p.Name)
-		}
-	} else {
-		polecatsToSync = []string{polecatName}
-	}
-
-	if len(polecatsToSync) == 0 {
-		fmt.Println("No polecats to sync.")
-		return nil
-	}
-
-	// Sync each polecat
-	var syncErrors []string
-	for _, name := range polecatsToSync {
-		// Get polecat to get correct clone path (handles old vs new structure)
-		p, err := mgr.Get(name)
-		if err != nil {
-			syncErrors = append(syncErrors, fmt.Sprintf("%s: %v", name, err))
-			continue
-		}
-
-		// Check directory exists
-		if _, err := os.Stat(p.ClonePath); os.IsNotExist(err) {
-			syncErrors = append(syncErrors, fmt.Sprintf("%s: directory not found", name))
-			continue
-		}
-
-		// Build sync command
-		syncArgs := []string{"sync"}
-		if polecatSyncFromMain {
-			syncArgs = append(syncArgs, "--from-main")
-		}
-
-		fmt.Printf("Syncing %s/%s...\n", rigName, name)
-
-		syncCmd := exec.Command("bd", syncArgs...)
-		syncCmd.Dir = p.ClonePath
-		output, err := syncCmd.CombinedOutput()
-		if err != nil {
-			syncErrors = append(syncErrors, fmt.Sprintf("%s: %v", name, err))
-			if len(output) > 0 {
-				fmt.Printf("  %s\n", style.Dim.Render(string(output)))
-			}
-		} else {
-			fmt.Printf("  %s\n", style.Success.Render("✓ synced"))
-		}
-	}
-
-	if len(syncErrors) > 0 {
-		fmt.Printf("\n%s Some syncs failed:\n", style.Warning.Render("Warning:"))
-		for _, e := range syncErrors {
-			fmt.Printf("  - %s\n", e)
-		}
-		return fmt.Errorf("%d sync(s) failed", len(syncErrors))
-	}
-
+	// With Dolt backend, beads changes are persisted immediately - no sync needed
+	fmt.Println("Note: With Dolt backend, beads changes are persisted immediately.")
+	fmt.Println("No sync step is required.")
 	return nil
 }