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/daemon/daemon.go

@@ -46,6 +46,7 @@ type Daemon struct {
 	cancel       context.CancelFunc
 	curator      *feed.Curator
 	convoyWatcher *ConvoyWatcher
+	doltServer   *DoltServerManager
 
 	// Mass death detection: track recent session deaths
 	deathsMu     sync.Mutex
@@ -93,6 +94,15 @@ func New(config *Config) (*Daemon, error) {
 		logger.Printf("Loaded patrol config from %s", PatrolConfigFile(config.TownRoot))
 	}
 
+	// Initialize Dolt server manager if configured
+	var doltServer *DoltServerManager
+	if patrolConfig != nil && patrolConfig.Patrols != nil && patrolConfig.Patrols.DoltServer != nil {
+		doltServer = NewDoltServerManager(config.TownRoot, patrolConfig.Patrols.DoltServer, logger.Printf)
+		if doltServer.IsEnabled() {
+			logger.Printf("Dolt server management enabled (port %d)", patrolConfig.Patrols.DoltServer.Port)
+		}
+	}
+
 	return &Daemon{
 		config:       config,
 		patrolConfig: patrolConfig,
@@ -100,6 +110,7 @@ func New(config *Config) (*Daemon, error) {
 		logger:       logger,
 		ctx:          ctx,
 		cancel:       cancel,
+		doltServer:   doltServer,
 	}, nil
 }
 
@@ -219,6 +230,10 @@ func (d *Daemon) heartbeat(state *State) {
 
 	d.logger.Println("Heartbeat starting (recovery-focused)")
 
+	// 0. Ensure Dolt server is running (if configured)
+	// This must happen before beads operations that depend on Dolt.
+	d.ensureDoltServerRunning()
+
 	// 1. Ensure Deacon is running (restart if dead)
 	// Check patrol config - can be disabled in mayor/daemon.json
 	if IsPatrolEnabled(d.patrolConfig, "deacon") {
@@ -292,6 +307,18 @@ func (d *Daemon) heartbeat(state *State) {
 	d.logger.Printf("Heartbeat complete (#%d)", state.HeartbeatCount)
 }
 
+// ensureDoltServerRunning ensures the Dolt SQL server is running if configured.
+// This provides the backend for beads database access in server mode.
+func (d *Daemon) ensureDoltServerRunning() {
+	if d.doltServer == nil || !d.doltServer.IsEnabled() {
+		return
+	}
+
+	if err := d.doltServer.EnsureRunning(); err != nil {
+		d.logger.Printf("Error ensuring Dolt server is running: %v", err)
+	}
+}
+
 // DeaconRole is the role name for the Deacon's handoff bead.
 const DeaconRole = "deacon"
 
@@ -666,6 +693,15 @@ func (d *Daemon) shutdown(state *State) error { //nolint:unparam // error return
 		d.logger.Println("Convoy watcher stopped")
 	}
 
+	// Stop Dolt server if we're managing it
+	if d.doltServer != nil && d.doltServer.IsEnabled() && !d.doltServer.IsExternal() {
+		if err := d.doltServer.Stop(); err != nil {
+			d.logger.Printf("Warning: failed to stop Dolt server: %v", err)
+		} else {
+			d.logger.Println("Dolt server stopped")
+		}
+	}
+
 	state.Running = false
 	if err := SaveState(d.config.TownRoot, state); err != nil {
 		d.logger.Printf("Warning: failed to save final state: %v", err)