In what way are we baptized into Jesus and His death? Through water baptism as 1 Pet 3:21 depicts. Through water and the Spirit as John 3:5 says. Through the baptism that man does and man receives as Matt 28:19 and Acts 2:38 state.
Nope through the Holy Spirit
Matthew 3:11 (KJV 1900) — 11 I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:
THE FORMING OF THE BODY The church is formed as believers are baptized by Christ with the Holy Spirit. For by one Spirit we were all baptized into one body. The Holy Spirit is the agent of baptism but Christ is the baptizer. At Jesus’ own baptism John the Baptist tells us that it is Jesus Christ, "He who is coming after me and is mightier than I," who would baptize "with the Holy Spirit and fire" (Matthew 3:11; cf. Mark 1:8; Luke 3:16; John 1:33). As explained in the following verse, the baptism of fire is the judgment of hell, the burning of "the chaff with unquenchable fire." As Savior, Christ baptizes with the Holy Spirit; as Judge, He baptizes with fire. All believers receive baptism with the Holy Spirit; all unbelievers will receive baptism with fire. Therefore every living soul will be baptized by Christ. Parenthetically, it should be noted that Paul is not speaking here of water baptism. Water baptism is an outward, physical ordinance believers submit to themselves and which is performed by other believers, in obedience to Christ’s command (Matthew 28:19; cf. Acts 2:38). Water baptism plays no part in conversion, but is a testimony to the church and to the world of conversion that has already taken place inwardly. Spirit baptism, on the other hand, is entirely the work of God and is virtually synonymous with salvation. The term baptizo ("to baptize") is used in the New Testament to refer to figurative immersion in trouble (Matthew 20:22-23, KJV) or to spiritual immersion (Romans 6:3-5) in Christ’s death and resurrection. As one can be immersed in water, so a believer is immersed spiritually into the Body of Christ. It should also be noted that the phrase "baptism of the Holy Spirit" is not a correct translation of any passage in the New Testament, including this one. En heni pneumati (by one Spirit) can mean "by or with one Spirit." Because believers are baptized by Christ, it is therefore best to translate this phrase as "with one Spirit." It is not the Holy Spirit’s baptism but Christ’s baptism with the Holy Spirit that gives us new life and places us into the Body when we trust in Christ. It is not possible to be a Christian and not be baptized by Christ with the Holy Spirit. Nor is it possible to have more than one baptism with the Spirit. There is only one Spirit baptism, the baptism of Christ with the Spirit that all believers receive when they are born again. By this the Son places all believers into the sphere of the Spirit’s power and Person, into a new environment, a new atmosphere, a new relationship with others, and a new union with Jesus Christ (cf. 1Corinthians 10:2, where Paul shows how the nation of Israel left Pharaoh and Egypt to become immersed and identified with a new leader, Moses, and a new land, Canaan). The pouring forth of the Holy Spirit at Pentecost also reveals that this baptism was by Jesus Christ (Acts 2:32-33), in fulfillment of John the Baptist’s prediction (Matthew 3:11; etc.) and of Jesus’ own promise (John 7:37-39; 15:7-15; Acts 1:5). We are not told exactly how this is done, any more than we are told exactly how God can give a person a new heart and new life. Those are mysteries beyond our comprehension. But there is no mystery as to the divine roles in salvation. The Father sent the Son and the Son sends the Spirit. The Son is the divine Savior, and the Holy Spirit is the divine Comforter, Helper, and Advocate. The Son is the baptizer and the Holy Spirit is the agent of baptism. Paul’s central point in 1Corinthians 12:13 is that baptism with the one Spirit makes the church one Body. If there were more than one Spirit baptism, there would be more than one church, and Paul’s whole point here would be destroyed. He is using the doctrine of baptism with the Spirit to show the unity of all believers in the Body. Many erring teachers today have used a wrong interpretation of the baptism with the Spirit to divide off from the Body an imagined spiritual elite who have what the rest do not. That idea violates the whole teaching here. For by one Spirit we were baptized into one body, whether Jews or Greeks, whether slaves or free. The apostle could not have stated the truth more clearly. One Spirit baptism establishes one church. There are no partial Christians, no partial members of Christ’s Body. The Lord has no halfway houses for His children, no limbo or purgatory. All of His children are born into His household and will forever remain in His household. "For you are all sons of God through faith in Christ Jesus. For all of you who were baptized into Christ have clothed yourselves with Christ" (Galatians 3:26-27). All believers in Jesus Christ become full members of His Body, the church, when they are saved. "There is one body and one Spirit, just as also you were called in one hope of your calling; one Lord, one faith, one baptism, one God and Father of all who is over all and through all and in all" (Ephesians 4:4-6). It is interesting that those who advocate Christians’ seeking the baptism by the Spirit in order to belong to the spiritual elite cannot seem to agree on how that is to be done. They have many ideas and many theories but no scriptural method. The reason is simple: Scripture contains no command, suggestion, or method for believers to seek or receive the baptism of the Spirit. You do not seek or ask for that which you already possess. The believers in Samaria who were converted under the ministry of Philip had to wait a short while to receive baptism with the Holy Spirit, until Peter and John came up to Samaria and laid hands on the converts (Acts 8:17). In that unique transitional situation as the church was beginning, those particular believers had to wait for the Holy Spirit, but they were not told to seek Him. The purpose for that exception was to demonstrate to the apostles, and to bring word back to the Jewish believers in general, that the same Holy Spirit baptized and filled Samaritan believers as baptized and filled Jewish believers — just as a short while later Peter and a few other Jewish Christians were sent to witness to Cornelius and his household in order to be convinced that the gospel was for all men and to see that "the Holy Spirit had been poured out upon the Gentiles also" (Acts 10:44-45). Those special transitional events did not represent the norm, as our present text makes clear, but were given to indicate to all that the Body was one (Acts 11:15-17).
The Holy Spirit is certainly active in baptism, but this is not "Spirit baptism"; it is water baptism. There is only one baptism in the NT Church (Eph 4:5), and it requires man to do it (Matt 28:19), it requires man to receive it (Acts 2:38), it requires water (1 Pet 3:21), it cannot be done passively (Acts 22:16), it includes both water and the Spirit (John 3:5).
Sorry there is no real baptism without the Holy Spirit
It is with the Holy Spirit one is baptized into the body of Christ
1 Corinthians 12:13 (NASB 2020) — 13 For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit.
Water will get you wet
The spirit will give you life and seal you in Christ
Ephesians 1:13–14 (NASB 2020) — 13 In Him, you also, after listening to the message of truth, the gospel of your salvation—having also believed, you were sealed in Him with the Holy Spirit of the promise, 14 who is a first installment of our inheritance, in regard to the redemption of God’s own possession, to the praise of His glory.