The Build wizard lists only Development, Ad Hoc, and In-House Distribution certificates and provisioning profiles.
The Publish wizard lists only App Store Distribution certificates and provisioning profiles.
This means that from the Build operation you will not be able to pick an App Store provisioning profile. You need to run the Publish operation instead. Keep in mind that the produced app package (IPA) will be downloadable but will be installable only from the App Store and you will not be really able to test in on any device.
However, your current subscription plan excludes the Publish operation and does not let you produce application packages for publishing (that is signed with an App Store distribution provisioning profile or built in Release mode). You can either upgrade your subscription or resort to using a third-party solution for code signing your application packages.
You can check the available pricing options here
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