I’ve had this problems a few times, and I’ve not been able to come to the bottom of what causes it. I think there might be some shenanigans caused when it’s started via dbus, vs. being started manually using a desktop item (although it should theoretically be the same binary from the same derivation reading the same configuration). Could you try killing the running instance, start fcitx5 via the application item and see if you get a different result? I’ll also assume you’re running X11?
You work magic… before I was opening the configtool, being prompted to start fcitx5 in the configtool and then mozc would be nowhere to be found. After killing it, starting it via dmenu and then editing my config, it suddenly shows up.