Brian --
I am not aware of any default functionality in Project for the Web to archive a completed project and then to hide it from other users. Keep in mind that this tool is still in its infancy, so maybe someday this functionality will be added. Until then, what I would do personally is to export every completed project to a Microsoft Excel workbook and then save those workbooks in a SharePoint site or a OneDrive file folder. And then I would delete all completed projects so that you can focus on what work needs to be done yet. Just an idea for you. Perhaps the others in this group will have some ideas for you as well. Hope this helps.