Seamonkey is "all your Internet needs in one application". Somewhat surprising it is still maintained

https://www.seamonkey-project.org/

Netscape Communicator perhaps?

Netscape Communicator certainly had the email features, but I don't think it ever included FTP. At most, it supported a primitive sort of web authoring via HTTP PUT requests (!).

Even Netscape Navigator (the browser-only version) had an FTP client built-in

Do you mean something beyond being able to load and display resources from FTP sites? I remember Netscape, and I also remember having to open up Fetch to do anything serious with FTP.