May I ask you how did you add Cangjie input method?
I’m using Italian and Japanese (Anthy) input methods on Fedora Workstation 39 and I can switch back and forth with meta-space without any issue anywhere.
Update:
I fresh install F38 workstation in virt-manager. meta-space works normally. Then Software prompts me to download F39. I followed the prompt, and updated to F39. Then meta-space failed to switch from Cangjie back to English.
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I add that using Gnome Software, by searching for Cangjie .