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/rig_dock.go

@@ -156,21 +156,12 @@ func runRigDock(cmd *cobra.Command, args []string) error {
 		return fmt.Errorf("setting docked label: %w", err)
 	}
 
-	// Sync beads to propagate to other clones
-	fmt.Printf("  Syncing beads...\n")
-	syncCmd := exec.Command("bd", "sync")
-	syncCmd.Dir = r.BeadsPath()
-	if output, err := syncCmd.CombinedOutput(); err != nil {
-		fmt.Printf("  %s bd sync warning: %v\n%s", style.Warning.Render("!"), err, string(output))
-	}
-
 	// Output
 	fmt.Printf("%s Rig %s docked (global)\n", style.Success.Render("✓"), rigName)
 	fmt.Printf("  Label added: %s\n", RigDockedLabel)
 	for _, msg := range stoppedAgents {
 		fmt.Printf("  %s\n", msg)
 	}
-	fmt.Printf("  Run '%s' to propagate to other clones\n", style.Dim.Render("bd sync"))
 
 	return nil
 }
@@ -234,14 +225,6 @@ func runRigUndock(cmd *cobra.Command, args []string) error {
 		return fmt.Errorf("removing docked label: %w", err)
 	}
 
-	// Sync beads to propagate to other clones
-	fmt.Printf("  Syncing beads...\n")
-	syncCmd := exec.Command("bd", "sync")
-	syncCmd.Dir = r.BeadsPath()
-	if output, err := syncCmd.CombinedOutput(); err != nil {
-		fmt.Printf("  %s bd sync warning: %v\n%s", style.Warning.Render("!"), err, string(output))
-	}
-
 	fmt.Printf("%s Rig %s undocked\n", style.Success.Render("✓"), rigName)
 	fmt.Printf("  Label removed: %s\n", RigDockedLabel)
 	fmt.Printf("  Daemon can now auto-restart agents\n")