Both Saul and Peter were Jews. Water baptism had been the well established norm for their thinking.
Keep in mind. John the Baptist was JEWISH!
People fail to realize that the Church age appeared out of nowhere and shocked many as it took everyone by surprise.
There was a need for a new learning curve! For it revolutionized the ways of thinking of those who had been comfortable
and well established in having been doing God's will until the big change (which came without notice) exploded upon them.
So.. sure! Peter and Paul would without hesitation been water baptizing according to the Jewish custom.
But, Peter who had been caught up in all the excitement previously finally realized what was going on only after water baptizing thousands..
“As I began to speak, the Holy Spirit came on them as he had come on us
at the beginning. Then I remembered what the Lord had said: ‘John baptized
with water, but you will be baptized with the Holy Spirit.’ So if God gave them
the same gift he gave us who believed in the Lord Jesus Christ, who was I to
think that I could stand in God’s way?”
When they heard this, they had no further objections and praised God, saying,
“So then, even to Gentiles God has granted repentance that leads to life.” Acts 11:15-18
See that? Peter who had been following the old way, had to finally adjust to the new way!
Then I remembered what the Lord had said: ‘John baptized with water,
but you will be baptized with the Holy Spirit.’
grace and peace!