fix: Add startup delay before nudging newly spawned polecats (gt-1dbcp)

Claude needs ~2 seconds to initialize before it can process nudges.
Without this delay, the initial "Work slung" message would arrive
before Claude was ready, causing the SessionStart hook not to fire.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

internal/cmd/sling.go

@@ -6,6 +6,7 @@ import (
 	"os"
 	"os/exec"
 	"strings"
+	"time"
 
 	"github.com/spf13/cobra"
 	"github.com/steveyegge/gastown/internal/beads"
@@ -13,6 +14,10 @@ import (
 	"github.com/steveyegge/gastown/internal/tmux"
 )
 
+// claudeStartupDelay is how long to wait for Claude to start before nudging.
+// This fixes gt-1dbcp: polecat auto-start doesn't process initial nudge.
+const claudeStartupDelay = 2 * time.Second
+
 var slingCmd = &cobra.Command{
 	Use:     "sling <bead-or-formula> [target]",
 	GroupID: GroupWork,
@@ -176,6 +181,12 @@ func runSling(cmd *cobra.Command, args []string) error {
 				}
 				targetAgent = spawnInfo.AgentID()
 				targetPane = spawnInfo.Pane
+
+				// Wait for Claude to start up before nudging (fixes gt-1dbcp)
+				if targetPane != "" {
+					fmt.Printf("Waiting for Claude to initialize...\n")
+					time.Sleep(claudeStartupDelay)
+				}
 			}
 		} else {
 			// Slinging to an existing agent
@@ -531,6 +542,12 @@ func runSlingFormula(args []string) error {
 				}
 				targetAgent = spawnInfo.AgentID()
 				targetPane = spawnInfo.Pane
+
+				// Wait for Claude to start up before nudging (fixes gt-1dbcp)
+				if targetPane != "" {
+					fmt.Printf("Waiting for Claude to initialize...\n")
+					time.Sleep(claudeStartupDelay)
+				}
 			}
 		} else {
 			// Slinging to an existing agent