Peter’s sermon in Acts 2 did talk about Jesus’ deity, but the point is slightly subtle. As you pointed out, Peter was speaking to about 3000 people, most of whom were Jewish. So the Jewish people had a bit of scriptural (Old Testament) background, which Peter referred to frequently in his sermon.
Let us take a look at the scriptural references which talk about Jesus’ deity.
The first reference was concerning what the prophet Joel said:
“The sun will be turned into darkness
And the moon into blood,
Before the great and glorious day of the Lord shall come.
And it shall be that everyone who calls on the name of the Lord will be saved.” (Acts 2:20-21)
In these verses, Peter is talking about Jesus’ second coming. Peter calls Jesus Lord, referring to the long-awaited Messiah the Jewish people were looking for. This Messiah is the one by whom people are eternally saved.
Now is this simply a person or is He divine? A common person cannot save us. But this Messiah saves humanity. Moreover, if we look at what the prophet Joel actually said in the Old Testament we find the following verses:
“The sun will be turned into darkness
And the moon into blood
Before the great and awesome day of the Lord comes.
And it will come about that whoever calls on the name of the Lord
Will be delivered...” (Joel 2:31-32)
The below link is the Hebrew interlinear Bible with the Hebrew text that the Old Testament was written in. Even though the New Testament was written in Greek, the Old Testament was written mostly in Hebrew. Therefore, we can look at the Hebrew text in Joel 2 and see that the word Lord in Greek (in Acts 2) refers to the word God in Hebrew (in Joel 2).
https://scripture4all.org/OnlineInterlinear/OTpdf/joe2.pdf
Every time the word “Lord” is used in the Hebrew text in Joel 2:31-32, the word Yahweh is used. We know that only God is referred to as Yahweh, which means “I am who I am” (Exodus 3:14).
Peter goes on to talk about Jesus’ divine abilities:
“But God raised Him up again, putting an end to the agony of death, since it was impossible for Him to be held in its power.” (v. 24)
Only God is able to conquer death. Peter goes on to say that even King David died (v. 29) and was buried, but this Jesus did not undergo decay (v. 27, 31).
Peter then referred to what David said: “The Lord said to my Lord…” (Psalm 110:1).
This in Hebrew translates to “Yahweh said to Adonai”. Both Yahweh and Adonai are names for God in the Old Testament.
Jesus Himself referred to this verse when He asked the Pharisees:
“ ‘What do you think about the Christ, whose son is He?’ They said to Him, ‘The son of David.’ He said to them, ‘Then how does David in the Spirit call Him “Lord,” saying,
‘The Lord said to my Lord,
“Sit at My right hand,
Until I put Your enemies beneath Your feet” ’?
If David then calls Him ‘Lord,’ how is He his son?’” (Matthew 22:42-45)
The answer to Jesus’ question is that Jesus Christ is both Son of God and Son of David (God incarnated in the flesh born of Mary who is a descendant of David). Jesus is Son of God, because David calls Him Lord.
So Peter told his audience that the Son of God, the Messiah the Jewish people were looking for, was the One whom they crucified!
“Therefore let all the house of Israel know for certain that God has made Him both Lord and Christ—this Jesus whom you crucified.” (v 36)
So Peter’s audience understood and realized they had crucified God. And “they were pierced to the heart” (v 37).
There are many other verses that proclaim Christ’s deity (see below). The word "Lord" in the New Testament, applied to Christ, does not simply mean Master. It means God.
"See to it that no one takes you captive through philosophy and empty deception, according to the tradition of men, according to the elementary principles of the world, rather than according to Christ. For in Him all the fullness of Deity dwells in bodily form, and in Him you have been made complete, and He is the head over all rule and authority; and in Him you were also circumcised with a circumcision made without hands, in the removal of the body of the flesh by the circumcision of Christ; having been buried with Him in baptism, in which you were also raised up with Him through faith in the working of God, who raised Him from the dead. " (Colossians 2:8-12)
"God, after He spoke long ago to the fathers in the prophets in many portions and in many ways, in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom also He made the world. And He is the radiance of His glory and the exact representation of His nature, and upholds all things by the word of His power. When He had made purification of sins, He sat down at the right hand of the Majesty on high, having become as much better than the angels, as He has inherited a more excellent name than they." (Hebrews 1:1-4)
Jesus also said: "Truly, truly, I say to you, before Abraham was born, I am" (John 8:58).
And Thomas said to Jesus: “My Lord and my God!” (John 20:28).