The Java Plugin for web browsers relies on the cross-platform plugin architecture NPAPI, which had been supported by all major web browsers for over a decade. Apple's Safari version 12 and above have dropped support for NPAPI, and therefore Java Plugin do not work on these browsers anymore.
Java applications are offered through web browsers as either a web start application (which do not interact with the browser once they are launched) or as a Java applet (which might interact with the browser). This change does not affect Web Start applications, it only impacts applets.
Developers and System administrators looking for alternative ways to support users of Safari should see this blog regarding Launching Web Start applications.