This feature has been requested by users a decade ago (JDK-8092115), but so far there seems to be no progress.
Now, to support the system tray, we need to use AWT. Frustratingly, this not only makes the program load and initialize more code, but it also hinders the generation of native-images for JavaFX applications. So I implore you to put system tray support in JavaFX on the agenda.