docs(priming): remove bd sync references for Dolt backend

Gas Town uses Dolt exclusively. Remove all bd sync and bd daemon
references from agent priming, templates, formulas, and docs.

With Dolt backend:
- Beads changes are automatically persisted
- No manual sync needed (no bd sync)
- No daemon needed (no bd daemon)

Updated files:
- polecat-CLAUDE.md template
- Role templates (crew, mayor, polecat)
- Message templates (spawn, nudge)
- Formulas (polecat-work, sync-workspace, shutdown, etc.)
- Reference docs

Part of hq-4f2f0c: Remove bd sync/daemon from agent priming

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/formula/formulas/mol-polecat-review-pr.formula.toml

@@ -254,13 +254,11 @@ Signal completion and clean up. You cease to exist after this step.
 
 **Self-Cleaning Model:**
 Once you run `gt done`, you're gone. The command:
-1. Syncs beads
-2. Nukes your sandbox
-3. Exits your session immediately
+1. Nukes your sandbox
+2. Exits your session immediately
 
 **Run gt done:**
 ```bash
-bd sync
 gt done
 ```
 
@@ -271,7 +269,7 @@ gt done
 
 You are NOT involved in any of that. You're gone. Done means gone.
 
-**Exit criteria:** Beads synced, sandbox nuked, session exited."""
+**Exit criteria:** Sandbox nuked, session exited."""
 
 [vars]
 [vars.pr_url]