For TL;DR, fcitx is not working on Manjaro + Gnome + Wayland.
Details: I could not find the stable version of Gnome edition. The official Manjaro homepage only had a Preview version for Gnome, so I downloaded it and updated everything.
Now, I want to type Japanese, but the default Ibus has some issues with Mozc Kana layout on English keyboard. Fcitx does not have this problem, and on Manjaro KDE edition, fcitx worked well. But unfortunately, KDE has problems with Wayland, so I installed the Gnome edition.
After installing fcitx, I can see its icon on the top bar, and I could run the configuration and add input languages. But it seems that I cannot switch to any languages in Wayland. In the fcitx icon on the top bar, if I click the input language item, there is no change. Shortcut keys are not working either.
If I log into Gnome Xorg, I can switch to one language, but still clicking the menu as in the previous paragraph has no change. What to do?