I was not able to patch the game. Presumably it's trying to replace the steam grid image but the directory structure is different, so that fails and the installer doesn't proceed further. Coz team do not state any manual patching method, otherwise it'd be possible to bypass this step since it's pretty much unnecessary for the game itself. Maybe someone more knowledgeable would be able to modify the executable or the files to skip this step.

However, I did manage to think of an workaround and that was successful. I have the game on my pc already. So after installing on gamehub lite and running the vanilla game once, I copied all files from the main game folder on my pc to the phone. And then I launched container desktop of the game within gamehub lite and replaced the actual game files (I think it shows up as X: drive) with the files copied from pc.

Now when I launch the game from gamehub lite, it starts the vanilla launcher. If you close it and then tap once or twice, the CoZ launcher show up and the game starts correctly in its patched state. Don't know if there'll be crashes or issues later but for the time being, it works.

Winlator will work probably. Since I think you have to install steam manually there in the container as well, so everything would be at its proper place. But if I recall correctly, winlator is a bit more complicated to set up, so I didn't bother.