To know the user's profile email address you need to specify the "identity.email" manifest permission, which results in the installation process warning that the extension can "Know your email address"
As a user who had received that warning, I would accept that my email address might be auto-filled in the login screen, but I would consider any emails I received to be unsolicited if I have not submitted my email address via the website. The law in any given jurisdiction might see it the same way.