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>

docs/INSTALLING.md

@@ -268,13 +268,13 @@ ssh -T git@github.com
 git config --global credential.helper cache
 ```
 
-### Beads sync issues
+### Beads issues
 
-If beads aren't syncing across clones:
+If experiencing beads problems:
 
 ```bash
 cd ~/gt/myproject/mayor/rig
-bd sync --status           # Check sync status
+bd status                  # Check database health
 bd doctor                  # Run beads health check
 ```
 

docs/reference.md

@@ -626,7 +626,6 @@ bd create --title="..." --type=task
 bd update <id> --status=in_progress
 bd close <id>
 bd dep add <child> <parent>  # child depends on parent
-bd sync                      # Push/pull changes
 ```
 
 ## Patrol Agents