Porknpie- As you said, this scripture tells us that ALL die in Adam. That is original sin. But the verse ends “so ALL will be made alive in Christ.” Christ overcame original sin for ALL.
Yes, Christ did die on the cross for OUR sins. That is why it is called the baptism of repentance for the remission of sins:
“John did baptise in the wilderness, and did teach the baptism for repentance for the remission of sins. And there went out unto him all the land of Judea, and they of Jerusalem, and were all baptized of him in the river of Jordon, confessing their sins.” (Mark 1:4-5)
When John baptised in the wilderness they didn’t confess Adam’s sins because Christ overcame the fall of Adam for ALL. They confessed, repented and were baptised for their own sins. Here again we see they were baptized in the river Jordon implying baptism by immersion. There is no reason to go down into a river otherwise.
Yes, we are made members of the body of Christ through baptism, but the above scriptures do not tell us we are cleansed of original sin by baptism. Christ over came original sin on the cross for everyone. “For as in Adam all die, even so in Christ shall all be made alive.” (1 Cor 15:22)