I’m using on of the listed SDK which they include a Privacy Manifest of their own, do I need to include one in my app or do I just use the third-party’s?
Ask the SDK developer for an updated version of the SDK that includes a privacy manifest. If your app needs a privacy manifest, add the file. Otherwise, do nothing.
From Privacy updates for App Store submissions:
Starting May 1: You’ll need to include approved reasons for the listed APIs used by your app’s code to upload a new or updated app to App Store Connect. If you’re not using an API for an allowed reason, please find an alternative. And if you add a new third-party SDK that’s on the list of commonly used third-party SDKs, these API, privacy manifest, and signature requirements will apply to that SDK. Make sure to use a version of the SDK that includes its privacy manifest and note that signatures are also required when the SDK is added as a binary dependency.