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“Incomplete and therefore incorrect”

No. To be “in Christ” has meaning. To continue:

“Therefore there is now no condemnation for those who are in Christ Jesus. 2 For the law of the Spirit of life in Christ Jesus has set you free from the law of sin and of death...

...However, you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. But if anyone does not have the Spirit of Christ, he does not belong to Him. 10 If Christ is in you, though the body is dead because of sin, yet the spirit is alive because of righteousness. 11 But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ Jesus from the dead will also give life to your mortal bodies through His Spirit who dwells in you.”

To repeat: “But if anyone does not have the Spirit of Christ, he does not belong to Him.”

ANYONE who belongs to Christ - who is “in Christ” to use the NT term - has the Spirit. It is the Baptism of the Holy Spirit that MAKES you a Christian:

“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.” - 1 Cor 12

And:

“So then, brethren, we are under obligation, not to the flesh, to live according to the flesh - 13 for if you are living according to the flesh, you must die; but if by the Spirit you are putting to death the deeds of the body, you will live. 14 For all who are being led by the Spirit of God, these are sons of God. 15 For you have not received a spirit of slavery leading to fear again, but you have received a spirit of adoption as sons by which we cry out, “Abba! Father!” 16 The Spirit Himself testifies with our spirit that we are children of God, 17 and if children, heirs also, heirs of God and fellow heirs with Christ, if indeed we suffer with Him so that we may also be glorified with Him.”

To repeat again: “The Spirit Himself testifies with our spirit that we are children of God, 17 and if children, heirs also, heirs of God and fellow heirs with Christ, if indeed we suffer with Him so that we may also be glorified with Him.”

We do not obey to become children of God. We become children of God so we will obey:

“For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; 9 not as a result of works, so that no one may boast. 10 For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand so that we would walk in them.” - Ephesians 2

There is no room for Purgatory. God’s sacrifice suffices:

“Christ did not therefore enter into any holy places made by human hands (however truly these may represent heavenly realities), but he entered Heaven itself to make his appearance before God as High Priest on our behalf. There is no intention that he should offer himself regularly, like the High Priest entering the holy of holies every year with the blood of another creature. For that would mean that he would have to suffer death every time he entered Heaven from the beginning of the world! No, the fact is that now, at this point in time, the end of the present age, he has appeared once and for all to abolish sin by the sacrifice of himself. And just as surely as it is appointed for all men to die and after that pass to their judgment, so it is certain that Christ was offered once to bear the sins of many and after that, to those who look for him, he will appear a second time, not this time to deal with sin, but to bring them to full salvation.”

“he has appeared once and for all to abolish sin by the sacrifice of himself”

Not future tense. Not, “he partially atones for some sins, and you will need to be purified from the rest”. To say that is to blaspheme the Holy Spirit, and deny the Holy Spirit’s testimony of Jesus Christ. Yet that is what Purgatory is rooted in - a partial and insufficient atonement so that man must may further payment for sin.