Did you check for a label on the bottom?

there was no label :(

I can't tell for certain from the picture, but it looks like the fabric is either microsuede or some kind of microfiber.

Do any of the cushions come off? If so, I'd remove one, flip it over and experiment with it a bit. The other option is to pay a professional upholstery cleaner to clean it. Good ones know enough about the fabric types to know how it should be cleaned.

Steam clean it. Will look great afterwards.

If you cannot remove the stains by cleaning, think about painting the fabric. Really! There are all kinds of tutorials online for using plain old latex paint mixed with fabric medium (available at craft stores) on upholstery to revive it. For example, but just google how to paint upholstered furniture

https://www.thekimsixfix.com/2014/05/how-to-paint-upholstery-latex-paint-and.html