If you specifically need a manual APK for a legacy device, reputable sites like APKMirror list both version 13.2.78 and the absolute latest builds. Google Play services 13.2.78 (000300-210410490) (000300)
Google Play Services version is an older release from around 2018. It is not the latest version. For modern Android devices (Android 6.0 and newer), Google Play Services updates automatically in the background to ensure your device remains secure and compatible with the newest apps. Key Features of Version 13.2.78 google play services 13.2.78 ultima version