.... The email must be associated with a Google Apps domain or Google group...
Apart from the gmail address of the project owner, you are only able to add an email from a domain which is tied to a
Google Workspace (formerly known as Google Apps for business or G-Suite) or a Google group (I believe the group is also as a result of a Google Workspace domain; not 100% sure of this)
As far as I know, there is no workaround to this. The theory is that GAE went this route to 'nudge' people towards 3rd party email providers (companies whose sole purpose is email provision) like Sendgrid, MailGun, MailJet, etc. See GAE
documentation for this. GAE users get a free quota from the providers listed on that page.