Thank you Brian (see article)! We can now change the default PWA site in Project Home.
This is a nice improvment, in the same direction than the permission mode being configurable from PWA settings (versus the SP CA). Now orgnizations tend to have more PWA sites and do need more flexibility to manage several PWA sites. This is also why proposing the new Project Home was very relevant.
From Project Home, you'll find this new "Default PWA site" option.
Then you can select a new PWA url.
When you select a PWA site, Project Online checks if the active account has the right permissions on the new defaut site.
Then what's new? When you'll create a new project from Project Home, it will use the new default PWA. Also the "Go to Project Web App" link will open the default PWA site.
If you are curious, you'll notice when you hit the "Go to Project Web App" that the URL is the following, using the "default" property.