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/doctor/beads_check.go

@@ -62,6 +62,7 @@ func (c *BeadsDatabaseCheck) Run(ctx *CheckContext) *CheckResult {
 	}
 
 	// If database file is empty but JSONL has content, this is the bug
+	// Note: This check is for SQLite backend; Dolt backend doesn't use these files
 	if dbErr == nil && dbInfo.Size() == 0 {
 		if jsonlErr == nil && jsonlInfo.Size() > 0 {
 			return &CheckResult{
@@ -72,7 +73,7 @@ func (c *BeadsDatabaseCheck) Run(ctx *CheckContext) *CheckResult {
 					"This can cause 'table issues has no column named pinned' errors",
 					"The database needs to be rebuilt from the JSONL file",
 				},
-				FixHint: "Run 'gt doctor --fix' or delete issues.db and run 'bd sync --from-main'",
+				FixHint: "Run 'gt doctor --fix' or delete issues.db and run 'bd import'",
 			}
 		}
 	}
@@ -113,6 +114,7 @@ func (c *BeadsDatabaseCheck) Run(ctx *CheckContext) *CheckResult {
 }
 
 // Fix attempts to rebuild the database from JSONL.
+// Note: This fix is for SQLite backend. With Dolt backend, this is a no-op.
 func (c *BeadsDatabaseCheck) Fix(ctx *CheckContext) error {
 	beadsDir := filepath.Join(ctx.TownRoot, ".beads")
 	issuesDB := filepath.Join(beadsDir, "issues.db")
@@ -128,8 +130,8 @@ func (c *BeadsDatabaseCheck) Fix(ctx *CheckContext) error {
 			return err
 		}
 
-		// Run bd sync to rebuild from JSONL
-		cmd := exec.Command("bd", "sync", "--from-main")
+		// Run bd import to rebuild from JSONL
+		cmd := exec.Command("bd", "import")
 		cmd.Dir = ctx.TownRoot
 		var stderr bytes.Buffer
 		cmd.Stderr = &stderr
@@ -152,7 +154,7 @@ func (c *BeadsDatabaseCheck) Fix(ctx *CheckContext) error {
 				return err
 			}
 
-			cmd := exec.Command("bd", "sync", "--from-main")
+			cmd := exec.Command("bd", "import")
 			cmd.Dir = ctx.RigPath()
 			var stderr bytes.Buffer
 			cmd.Stderr = &stderr

internal/doctor/rig_check.go

@@ -844,46 +844,19 @@ func (c *BeadsConfigValidCheck) Run(ctx *CheckContext) *CheckResult {
 		}
 	}
 
-	// Check sync status
-	cmd = exec.Command("bd", "sync", "--status")
-	cmd.Dir = c.rigPath
-	output, err := cmd.CombinedOutput()
-	c.needsSync = false
-	if err != nil {
-		// sync --status may exit non-zero if out of sync
-		outputStr := string(output)
-		if strings.Contains(outputStr, "out of sync") || strings.Contains(outputStr, "behind") {
-			c.needsSync = true
-			return &CheckResult{
-				Name:    c.Name(),
-				Status:  StatusWarning,
-				Message: "Beads out of sync",
-				Details: []string{strings.TrimSpace(outputStr)},
-				FixHint: "Run 'gt doctor --fix' or 'bd sync' to synchronize",
-			}
-		}
-	}
+	// Note: With Dolt backend, there's no sync status to check.
+	// Beads changes are persisted immediately.
 
 	return &CheckResult{
 		Name:    c.Name(),
 		Status:  StatusOK,
-		Message: "Beads configured and in sync",
+		Message: "Beads configured and accessible",
 	}
 }
 
-// Fix runs bd sync if needed.
+// Fix is a no-op with Dolt backend (no sync needed).
 func (c *BeadsConfigValidCheck) Fix(ctx *CheckContext) error {
-	if !c.needsSync {
-		return nil
-	}
-
-	cmd := exec.Command("bd", "sync")
-	cmd.Dir = c.rigPath
-	output, err := cmd.CombinedOutput()
-	if err != nil {
-		return fmt.Errorf("bd sync failed: %s", string(output))
-	}
-
+	// With Dolt backend, beads changes are persisted immediately - no sync needed
 	return nil
 }