Since I came to Korea I struggled to use the Korean Alphabet on my Linux machine with GNOME. Fcitx 5 is the one which has least problems with Korean, but there is a bug in GNOME which prevents me to use it in the search box to start applications https://gitlab.gnome.org/GNOME/gnome-shell/-/issues/797 The bug is open and already 6 years old, so I don't think it will be fixed soon.

Anyway, Sungjoon Moon who reached out to me because of my blog post https://jeena.net/scaling-on-linux has also given a talk "Status of CJK input system in Wayland" check it out: https://fosdem.org/2025/schedule/event/fosdem-2025-6533-status-of-cjk-input-system-in-wayland/

He shows some of the bugs of it in different apps, and the problems why those bugs are still there.