There are other guides on how to do this, but they are pretty clunky (I believe I saw one using a virtual Ubuntu environment?). The below guide works for using mozc with GNOME on Wayland, although I expect that it can be easily adapted for other environments.
I use Nix to supplement swupd
for less often-used packages. I recommend using the Determinate Systems installer (for this guide, you will need flakes enabled which this automatically does for you).
If you don't have Home Manager installed:
nix profile install nixpkgs#ibus-engines.mozc
Otherwise, add it to your home.packages
.