feat: add structured logging with log/slog and panic recovery

Replace log.Printf/Println with slog.Info/Error/Warn across the codebase.
Initialize slog with JSON handler in main.go. Add panic recovery defer
in SSH session handler. Add structured game event logging (room created,
player joined, game started, game over, player inactive removed).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

game/lobby.go

@@ -2,6 +2,7 @@ package game
 
 import (
 	"fmt"
+	"log/slog"
 	"math/rand"
 	"sync"
 
@@ -138,6 +139,7 @@ func (l *Lobby) CreateRoom(name string) string {
 		Name:   name,
 		Status: RoomWaiting,
 	}
+	slog.Info("room created", "code", code, "name", name)
 	return code
 }
 
@@ -155,6 +157,7 @@ func (l *Lobby) JoinRoom(code, playerName, fingerprint string) error {
 		return fmt.Errorf("room %s already in progress", code)
 	}
 	room.Players = append(room.Players, LobbyPlayer{Name: playerName, Fingerprint: fingerprint})
+	slog.Info("player joined", "room", code, "player", playerName)
 	return nil
 }
 
@@ -218,6 +221,7 @@ func (l *Lobby) StartRoom(code string) {
 	defer l.mu.Unlock()
 	if room, ok := l.rooms[code]; ok {
 		room.Status = RoomPlaying
+		slog.Info("game started", "room", code, "players", len(room.Players))
 	}
 }