During some testing I did, I installed fcitx-hangul and restarted the PC. Fcitx5 doesn't appear in the Virtual Keyboard settings, which is what I usually enable on KDE so that I can setup fcitx on the panel and add Hangul. The tray icon was unresponsive and still appeared after I uninstalled fcitx-hangul. I tried to use ibus-hangul instead but layout switching didn't work, but works fine in Budgie and GNOME. Does fcitx work with Solus KDE? I haven't found anyone else with this specific issue.
Edit: This happened on a fresh install of Solus 4.6.