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>

templates/polecat-CLAUDE.md

@@ -156,7 +156,6 @@ gt mail send <addr> -s "Subject" -m "Body"
 bd show <id>                # View issue details
 bd close <id> --reason "..." # Close issue when done
 bd create --title "..."     # File discovered work (don't fix it yourself)
-bd sync                     # Sync beads to remote
 ```
 
 ---
@@ -191,8 +190,7 @@ When your work is done, follow this EXACT checklist - **step 5 is REQUIRED**:
        - For Go projects:    go test ./... && go vet ./...
 [ ] 2. Stage changes:     git add <files>
 [ ] 3. Commit changes:    git commit -m "msg (issue-id)"
-[ ] 4. Sync beads:        bd sync
-[ ] 5. Self-clean:        gt done   ← MANDATORY FINAL STEP
+[ ] 4. Self-clean:        gt done   ← MANDATORY FINAL STEP
 ```
 
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