The issue can be seen on Mac Ventura 13.1 (windows, linux - TBD) with a secondary monitor set to a different scale.
The primary retina screen has scale=2, the secondary one has scale=1.

To reproduce:
- configure the external monitor to have scale = 1.
- add a Japanese keyboard in Settings -> Keyboard -> Text Input -> Input Sources (Japanese - Romaji)
- run attached program
- click on the text field
- press fn/🌐 key to switch input method to Japanese (alternatively, use the main toolbar [A] icon to switch the input method from a pulldown.
- type "arigatou"
- notice that the IME window appears below the text field near caret. It does so on the primary screen.
- move the window to the secondary screen where scale == 1.
- type in "arigatou"
===> notice that the window appears above the text field, sometimes even outside of the main window.

The issue can be seen in javafx-sdk-19.0.2.1, and possibly earlier.

It is unclear whether it's a Mac-specific bug or it affects all the platforms.