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-conflict-resolve.formula.toml

@@ -306,11 +306,6 @@ bd close <source-issue> --reason="merged via conflict resolution"
 The Refinery normally closes issues after merge, but since we pushed
 directly to main, we handle it here.
 
-**3. Sync beads:**
-```bash
-bd sync
-```
-
 **Exit criteria:** Original MR and source issue are closed."""
 
 [[steps]]