The
macOS download page does say, "calibre works on macOS 10.14 (Mojave) and higher". This is right at the top underneath the "Download for macOS" header. Plus note #3 at the bottom reads: "If you are using macOS older than 10.14 (Mojave), the last version of calibre that will work on your machine is 3.48, available here."
As for Catalina, Kovid has reported that he
succeeded in notarizing Calibre 4, so it should work, theoretically.