Symptoms
You are unable to migrate the structure of your Project Web App (PWA) site and/or your Project Site.
Details
PWA is a server-based application. Creating a PWA site with a new site collection creates a PWA database on a specified instance of Microsoft's Project Server.
Project Sites are a SharePoint site template that uses a PWA frame. The structure of your Project Site does not exist in SharePoint but in the Project Server.
The migration of PWA environments, including Project Sites, is not supported by the ShareGate migration tool because the architecture is server-based and not SharePoint-based. All features specific to Project Server cannot be migrated.
Solution
Create a PWA environment or Project Site at your destination and use Copy content only to migrate the items and documents of your source.
Features such as custom lists, links, any automation, or Web Parts, may not be handled properly and will need to be rebuilt manually at your destination.