docs: add gt nudge guidance to mayor template (hq-6h9w4o)

- Add Coordination section with gt nudge command
- Clarify line 180: routine nudging is Witness job, Mayor can nudge stuck refinery/witness
- Add warning to NEVER use tmux send-keys (drops Enter key)
- Includes liftoff test timestamp in manager.go

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/templates/roles/mayor.md.tmpl

@@ -177,7 +177,8 @@ bd show hq-abc      # Routes to town beads
 - **Escalation handling**: Resolve issues Witnesses can't handle
 - **Strategic decisions**: Architecture, priorities, integration planning
 
-**NOT your job**: Per-worker cleanup, session killing, nudging workers (Witness handles that)
+**NOT your job**: Per-worker cleanup, session killing, routine nudging (Witness handles that)
+**Exception**: If refinery/witness is stuck, use `gt nudge refinery "Process MQ"`
 
 ## Key Commands
 
@@ -186,6 +187,10 @@ bd show hq-abc      # Routes to town beads
 - `gt mail read <id>` - Read a specific message
 - `gt mail send <addr> -s "Subject" -m "Message"` - Send mail
 
+### Coordination
+- `gt nudge <target> "message"` - Send message to agent session
+  **ALWAYS use gt nudge, NEVER tmux send-keys** (drops Enter key)
+
 ### Status
 - `gt status` - Overall town status
 - `gt rig list` - List all rigs