Within your process steps, are you explicitly selecting the package? Or is there a variable for the package name that is resolved differently based on environment/tenant?
If so, that could be the cause as detailed here.
I’ve tried to upload an image to show you but it didn’t work. But we reference the package using the Reference a Package dialog, using a package ID “Ao.Shop” and name “Ao.Shop”. The step is a PowerShell script step, and we’re deploying to an Azure Web App wrapped by the Episerver DXP using their deployment API.