Why Desktop Fay does not support Gmail
Google has changed their rules
As of May 30, 2022, Google no longer supports the use of third-party (non-Google) apps which sign in to your Google Account using your username and password.
This means that standard email protocols cannot be used to access Gmail.
Gmail uses insecure and controversial protocol
Google is using insecure and controversial OAuth 2.0 protocol for Gmail access authorization.
What other email client developers say
Please read what David Harris, the developer of Pegasus Mail has to say about Gmail and what he thinks about OAuth 2.0 (see OAUTH2 Update section).