Romans 3:28 talks about being justified by faith apart from works of the law. That’s what people mean when they say baptism doesn’t save.
Salvation comes through the spiritual transformation in your heart. Baptism is beautiful and important, but it’s a demonstration of what’s already happened inside you.
Following Christ is the goal. Everything else flows from that, baptism included.
I had been saved for a while before I even thought about water baptism. But after reading how the apostles talked about it, I went ahead and did it. The water didn’t change anything inside me, but it was still something I wanted to do between me and God.
Read Mark 16:16 closely. The condemnation half only mentions not believing. Skipping the water gets no mention at all.