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-deacon-patrol.formula.toml

@@ -419,114 +419,10 @@ gt mail send mayor/ -s "Health: <rig> <component> unresponsive" \\
 
 Reset unresponsive_cycles to 0 when component responds normally."""
 
-[[steps]]
-id = "hung-session-detection"
-title = "Detect and recover hung Gas Town sessions (SURGICAL)"
-needs = ["health-scan"]
-description = """
-Detect and surgically recover hung Gas Town sessions where the Claude API call is stuck.
-
-A hung session appears "running" (tmux session exists, Claude process exists) but
-the API call has been stuck indefinitely. This breaks patrol chains - if witness
-hangs, refinery never gets nudged about new MRs.
-
-**Why existing checks miss this:**
-- zombie-scan only catches processes not in tmux sessions
-- gt status shows "running" if tmux session exists
-- Nudges queue but never get processed (Claude can't respond)
-
-## SURGICAL TARGETING
-
-**ONLY these session patterns are valid targets:**
-- `gt-<rig>-witness` (e.g., gt-kalshi-witness, gt-horizon-witness)
-- `gt-<rig>-refinery` (e.g., gt-kalshi-refinery)
-- `hq-deacon`
-
-**NEVER touch sessions that don't match these patterns exactly.**
-
-## DETECTION (All checks must pass)
-
-For each Gas Town session, capture output and verify ALL of these:
-
-```bash
-# Step 1: Get session output
-output=$(tmux capture-pane -t <session-name> -p 2>/dev/null | tail -10)
-```
-
-**Check 1: Session is in waiting state**
-Must see one of: `Clauding`, `Deciphering`, `Marinating`, `Finagling`, `thinking`
-```bash
-echo "$output" | grep -qiE 'Clauding|Deciphering|Marinating|Finagling|thinking'
-```
-
-**Check 2: Duration exceeds threshold (30+ minutes)**
-Parse duration from output like "21h 35m 20s" or "45m 30s":
-```bash
-# Extract hours and minutes
-hours=$(echo "$output" | grep -oE '[0-9]+h' | head -1 | tr -d 'h')
-minutes=$(echo "$output" | grep -oE '[0-9]+m' | head -1 | tr -d 'm')
-total_minutes=$((${hours:-0} * 60 + ${minutes:-0}))
-# Threshold: 30 minutes minimum
-[ "$total_minutes" -ge 30 ]
-```
-
-**Check 3: Zero tokens received (definite hang) OR very long duration (>2 hours)**
-```bash
-# Definite hang: zero tokens received
-echo "$output" | grep -qE '↓ 0 tokens'
-# OR extremely long duration (>2 hours = 120 minutes)
-[ "$total_minutes" -ge 120 ]
-```
-
-**Check 4: NOT showing active tool execution**
-Active sessions show tool markers (⏺). If present, session is actually working:
-```bash
-# If tool markers present in recent output, DO NOT kill
-echo "$output" | grep -qE '⏺|Read|Write|Bash|Edit' && continue
-```
-
-## RECOVERY (Only after ALL checks pass)
-
-**Log the action first:**
-```bash
-echo "[$(date)] RECOVERING HUNG: <session-name> (${hours}h ${minutes}m, waiting state)" >> $GT_ROOT/logs/hung-sessions.log
-```
-
-**Kill and restart based on session type:**
-
-For witness:
-```bash
-tmux kill-session -t gt-<rig>-witness 2>/dev/null
-gt witness start <rig>
-```
-
-For refinery:
-```bash
-tmux kill-session -t gt-<rig>-refinery 2>/dev/null
-gt refinery restart <rig>
-```
-
-For deacon (self-recovery - use with caution):
-```bash
-# Deacon detecting itself is hung is a paradox
-# Only kill if another deacon instance exists or human confirmed
-gt mail send mayor/ -s "DEACON SELF-HUNG DETECTED" -m "Deacon appears hung. Human intervention required."
-```
-
-## VERIFICATION
-
-After restart, verify new session is healthy:
-```bash
-sleep 5
-tmux has-session -t <session-name> && echo "Session restarted successfully"
-```
-
-**Exit criteria:** All hung Gas Town sessions detected and recovered (or escalated if recovery failed)."""
-
 [[steps]]
 id = "zombie-scan"
 title = "Detect zombie polecats (NO KILL AUTHORITY)"
-needs = ["hung-session-detection"]
+needs = ["health-scan"]
 description = """
 Defense-in-depth DETECTION of zombie polecats that Witness should have cleaned.