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/lifecycle.go

@@ -604,22 +604,7 @@ func (d *Daemon) syncWorkspace(workDir string) {
 		// Don't fail - agent can handle conflicts
 	}
 
-	// Reset stderr buffer
-	stderr.Reset()
-
-	// Sync beads
-	bdCmd := exec.Command("bd", "sync")
-	bdCmd.Dir = workDir
-	bdCmd.Stderr = &stderr
-	bdCmd.Env = os.Environ() // Inherit PATH to find bd executable
-	if err := bdCmd.Run(); err != nil {
-		errMsg := strings.TrimSpace(stderr.String())
-		if errMsg == "" {
-			errMsg = err.Error()
-		}
-		d.logger.Printf("Warning: bd sync failed in %s: %s", workDir, errMsg)
-		// Don't fail - sync issues may be recoverable
-	}
+	// Note: With Dolt backend, beads changes are persisted immediately - no sync needed
 }
 
 // closeMessage removes a lifecycle mail message after processing.