Acts 2:38 says exactly the same thing as well. Consider this version:
“Kefa answered them, “Turn from sin, return to God, and each of you be immersed on the authority of Yeshua the Messiah into forgiveness of your sins, and you will receive the gift of the Ruach HaKodesh!”
Acts of Emissaries of Yeshua (Act) 2:38 CJB
https://bible.com/bible/1275/act.2.38.CJB
The Greek word for repent is metanoesate. It means to have a change of mind or to think differently. In order to believe a persons mind is changed. So, belief represents the change in thinking.
What does it mean to be immersed into forgiveness of sins? Consider this verse.
“In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace,”
Ephesians 1:7 ESV
https://bible.com/bible/59/eph.1.7.ESV
Immersion into forgiveness of sins is immersion into Christ.
So, Acts 2:38 says this:
Change your mind, or believe if you will, and be immersed on the authority of Jesus Christ into forgiveness of sins, or into Christ.
The gift of the Holy Spirit is our immersion into Christ and the forgiveness that brings.
Total agreement with 1 John 5:1, Mark 16:16, Ephesians 1:13
So, if we understand that metanoesate means to have a change of mind, that Baptistheto means to immerse, and that the primary meaning of eis is into, we can see Acts 2:38 very differently.