That pink slime is biofilm — a layer of bacteria that builds up on surfaces in standing or moving water. The reason it took over your old fountain is the plastic: plastic is soft and porous, so bacteria work their way into tiny scratches and pores and stay there, no matter how hard you scrub.
Stainless steel is the opposite — it's a hard, non-porous surface with nowhere for bacteria to dig in, so it blocks up to 99% of bacteria and the slime never gets the same foothold. You'll still want to rinse it and swap the filter regularly (every surface needs basic cleaning), but you won't be fighting that slimy pink film every week like you were with plastic.