Fix spawn priming race: use deacon patrol instead of broken nudge (gt-6957)

- Remove 3-second sleep and NudgeSession from spawn.go
  (Claude takes 10-20s to initialize, message arrived too early)
- Add trigger-pending-spawns step to deacon patrol molecule
  (Deacon polls with WaitForClaudeReady, sends trigger when ready)
- SessionStart hook handles gt prime (internal, reliable)
- Deacon sends minimal 'Begin.' trigger to start polecat working

The spawn command now returns immediately after starting the session.
The deacon's patrol cycle will trigger the polecat when it's ready.

internal/beads/builtin_molecules.go

@@ -632,6 +632,31 @@ gt mail read <id>
 
 Callbacks may spawn new polecats, update issue state, or trigger other actions.
 
+## Step: trigger-pending-spawns
+Nudge newly spawned polecats that are ready for input.
+
+When polecats are spawned, their Claude session takes 10-20 seconds to initialize.
+The spawn command returns immediately without waiting. This step finds spawned
+polecats that are now ready and sends them a trigger to start working.
+
+` + "```" + `bash
+# For each rig with polecats
+for rig in gastown beads; do
+    gt polecats $rig
+    # For each working polecat, check if Claude is ready
+    # Use tmux capture-pane to look for "> " prompt
+done
+` + "```" + `
+
+For each ready polecat that hasn't been triggered yet:
+1. Send "Begin." to trigger UserPromptSubmit hook
+2. The hook injects mail, polecat sees its assignment
+3. Mark polecat as triggered in state
+
+Use WaitForClaudeReady from tmux package (polls for "> " prompt).
+Timeout: 60 seconds per polecat. If not ready, try again next cycle.
+Needs: inbox-check
+
 ## Step: health-scan
 Ping Witnesses and Refineries.
 
@@ -649,7 +674,7 @@ done
 ` + "```" + `
 
 Report any issues found. Restart unresponsive components if needed.
-Needs: inbox-check
+Needs: trigger-pending-spawns
 
 ## Step: plugin-run
 Execute registered plugins.