No it's the opposite as far as I understand it: "P. aeruginosa has evolved a variety of zinc transport systems that enable it to thrive in zinc-deficient environments and during infection" So allegedly Zinc encourages pseudomonas (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8456098/
I think it's the same with Iron - pseudomonas eats iron too allegedly!