Kate does not work well with keyboard navigation. https://mail.kde.org/pipermail/kde-accessibility/2018-November/003253.html
I can confirm that with Kate (unlike other applications the key press for up keys is seemingly not sent. The Qt stuff uses a relatively crude global event filter, presumably that's where to look. This is not technically related to Plasma, but I don't feel like staring a new board, but want to track this somewhere.