When copying an entire site, Sharegate does not automatically copy master pages and page layouts. The reason for this is that master pages and page layouts will not work as-is if they are migrated from one version of SharePoint to another. Unfortunately, Sharegate does not support updating them so that they work in the new version of SharePoint.
Master pages and page layouts can still be copied using the Copy SharePoint Content tool this way:
- Connect to the root site of the source site collection and select the Master Page Gallery, then click Next.
- Connect to the root site of the destination site collection and select the Master Page Gallery, then click next.
- Select the specific master pages and page layouts to copy and drag & drop them to the destination.
It is important to only select the elements that you specifically want to migrate, since overwriting all the default master pages and page layouts can easily lead to errors. Also, master pages and page layouts copied between different versions of SharePoint will most likely need to be modified manually in order to work correctly.