Some only let Compose < - (←) work, stopping and preventing Compose < - > (↔) from working. Others, if I remember correctly, let Compose < - Enter work to get ←.
Once an Input Method is involved, it can handle the Compose key, and that’s what fcitx5 is doing for me now, so that everything’s behaving the same… but that “same” is not what I reckon it should be.