feat: add gt mail check command and update prime for GGT cutover

- Add 'gt mail check' with --inject flag for Claude Code hooks
- Update Mayor prime output to include mail commands and startup info
- Enables full cutover from PGT 'town' commands to GGT 'gt' commands

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

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

internal/cmd/prime.go

@@ -156,10 +156,15 @@ func outputMayorContext(ctx RoleContext) {
 	fmt.Println("- Monitor overall system health")
 	fmt.Println()
 	fmt.Println("## Key Commands")
+	fmt.Println("- `gt mail inbox` - Check your messages")
+	fmt.Println("- `gt mail read <id>` - Read a specific message")
 	fmt.Println("- `gt status` - Show overall town status")
 	fmt.Println("- `gt rigs` - List all rigs")
 	fmt.Println("- `bd ready` - Issues ready to work")
 	fmt.Println()
+	fmt.Println("## Startup")
+	fmt.Println("Check for handoff messages with 🤝 HANDOFF in subject - continue predecessor's work.")
+	fmt.Println()
 	fmt.Printf("Town root: %s\n", style.Dim.Render(ctx.TownRoot))
 }