refactor: extract shared player.ID type and GenerateID to player package

Both game and snake packages had identical PlayerID types and the snake
package imported game.GenerateID. Now both use player.ID and
player.GenerateID from the shared player package.

player/player.go

@@ -0,0 +1,18 @@
+// Package player provides shared identity types used across game packages.
+package player
+
+import (
+	"crypto/rand"
+	"encoding/hex"
+)
+
+// ID uniquely identifies a player within a session. For authenticated users
+// this is their user UUID; for guests it's a random hex string.
+type ID string
+
+// GenerateID returns a random hex string of 2*size characters.
+func GenerateID(size int) string {
+	b := make([]byte, size)
+	_, _ = rand.Read(b)
+	return hex.EncodeToString(b)
+}