I've never used that printer or Cachy OS. That being said, I don't think installing HP printer software will help with an Epson printer.
Epson do have printer drivers for linux and you can look up your specific printer download here https://download-center.epson.com/search/
Most distros include a tool to convert or install packages from other formats. I'd look into that. I've never used Arch so unfortunately I can't be more specific.