This is usually because both packages have files at identical locations and so allowing you to install both would mean one would partially get overwritten by the other.
I did a little searching and found that wine-cachyos now includes wine-mono, so you will want to uninstall wine-mono (as well as wine-gecko apparently according to this thread) by answering the prompt with "Y". I assume it will also prompt you about wine-gecko so you should be able to just answer the prompts with Y and it should work.