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/beads/beads.go

@@ -747,18 +747,15 @@ This is physics, not politeness. Gas Town is a steam engine - you are a piston.
 - ` + "`gt mol status`" + ` - Check your hooked work
 - ` + "`gt mail inbox`" + ` - Check for messages
 - ` + "`bd ready`" + ` - Find available work (no blockers)
-- ` + "`bd sync`" + ` - Sync beads changes
 
 ## Session Close Protocol
 
 Before signaling completion:
 1. git status (check what changed)
 2. git add <files> (stage code changes)
-3. bd sync (commit beads changes)
-4. git commit -m "..." (commit code)
-5. bd sync (commit any new beads changes)
-6. git push (push to remote)
-7. ` + "`gt done`" + ` (submit to merge queue and exit)
+3. git commit -m "..." (commit code)
+4. git push (push to remote)
+5. ` + "`gt done`" + ` (submit to merge queue and exit)
 
 **Polecats MUST call ` + "`gt done`" + ` - this submits work and exits the session.**
 `