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>

.beads/PRIME.md

@@ -28,16 +28,13 @@ 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 saying "done":
 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)
+3. git commit -m "..." (commit code)
+4. git push (push to remote)
 
-**Work is not done until pushed.**
+**Work is not done until pushed.** Beads changes are automatically committed with Dolt.