The gospel preaching in the book of Acts called souls to repentance, but it was a basic repentance of faith
I, incidentally, don't agree with that. The accusation of the Jews was indeed collective, but it was utterly grave: "let all the house of Israel know most certainly, that God hath made both Lord and Christ, this same Jesus, whom you have crucified" (Acts 2:36).
The “basic repentance of faith” was in regards to turning to Christ as Lord and Saviour, out of which a life which corresponded to that faith came, rather than a detailed list of all the sins they had to quit in order to come to Christ, as only be doing the latter with a contrite heart can they walk in victory over sins.
The sermon then calls them not to simply declare Jesus as Lord and Savior -- after the Evangelical fashion -- but rather "Do penance [or if you wish, "repent"], and be baptized every one of you in the name of Jesus Christ, for the remission of your sins". Further, this echoes the words of St. John the Baptist, but the kind of penance he called for is not in any way "basic" or matter of "recognizing" the lordship of Christ. Rather, he wore a hairshirt, fasted and was a celibate hermit,-- the harshest forms of penance known to us.
Where in the world do you get penance (voluntary self-punishment) out of repentance in Acts 2:38? The DRB wrongly renders it as such, while the official Roman Catholic Bible rightly states “repent,” and the word occurs 34 times, and essentially means a change of mind. While this results in a change of life, it is used in distinction from the actual works, as in Acts 26:20, “that they should repent and turn to God, and do works meet [corresponding to] for repentance.”
Peter is not telling them to go do works of self affliction and be baptized to be forgiven and receive the Holy Spirit, but to repent from their unbelief and believe on the One they crucified, which faith decision is signified by being baptized in the name of the Lord Jesus. That he did not tell them to do penance to be saved is clear, as what they did not do to be born again was go out and do works of self-affliction, but were immediately baptized, which signified repentance. And which they then evidenced by continuing in the faith.
As for how the Baptist lived, you are mistaking what practically results from conversion with with what is required to be converted. The Baptist did so to chasten himself, and thus Paul worked to keep under his body, and historic evangelical preaching abounded in this call to self denial.
Says "Pœnitentiam agite". The only official Bible is the Latin translation or the Greek original. The Greek original says μετανοειτε.
The only guidance of whether μετανοειτε refers to a physical act of penance is in the acts of St. John the Baptist. St. Peter, as Acts 2:38 reports, likewise directed the Jews to baptism for the remission of their sins. To suggest that the "changing of the mind" was purely an intellectual exercise is not biblical.
In Acts 26:20, “that they should repent and turn to God, and do works meet [corresponding to] for repentance.” -- corroborates the fact that the Bible teaches "metanoia" as something people DO rather than think or feel. "Do penance" is the proper translation, it reflects the active nature of true penance.