There is no readily apparent resolution to this paradox.
As instruction is given but no one, in the entire NT, ever followed this instruction as far as the record shows.
There is little reason however to think the instruction is a corruption.
If the current (longer) manuscript reading of Matthew 28 is not correct, that would mean that all the “correct” manuscripts, and the literature of the early church including the quotations of Matthew 28:19 in the writings of the Church Fathers, would have had to have been destroyed or altered, and in general the early church was too fragmented and not centralized enough for that to happen (for a more compete discussion of this, see “Is Matthew 28:19 a Forgery” by Sean Finnegan on biblicalunitarian.com).
What is often inferred unfortunately, that this is a good proof-text for those believing the Holy Spirit is a person/entity apart from the Father simply because it is named alongside the Father and the son. Of course, that is only by inference as Matthew 28:18-20 says nothing about this matter. Unfortunately, it then sits alongside (by association) the 1John 5:7b which is an absolute corruption.
the Father, the Word, and the Holy Spirit; and these three are one.
The disciples understood the Holy Spirit and the Father were descriptors of the same 'one true God' that Jesus referred to. John 17:3
When one is baptised into the name of Jesus - as all the Apostles did, we die (by immersion) with him as he died, and we live with him as we arise from the water as he now lives.
This symbolism of the new life automatically joins one to the Father through Jesus, and by the new holy spirit life (1Pet 3:18) dwelling in that one at the new birth. God, the Father, is present in the person via the son and God's spirit. In this age we only have the deposit of God's spirit as a down-payment of the fullness yet to be given (2Cor 1:22, 5:5).
So while there remains a paradox that has no solid explanation, we must be careful to not extrapolate the words given to make up erroneous doctrine based on imagination and speculative ideas.
Baptising one in the name of Jesus, carried with that name great authority. God has given Jesus all authority under Him to manage everything! So we can understand that by noting the name of the Father and the holy spirit (which has no name) the authority Jesus has is affirmed by the One from whom it came - his God and Father, John 20:17 etc.
And Jesus came up and spoke to them, saying, “All authority in heaven and on earth has been given to me. Matt 28:18
Clearly he didn't always have this authority as he could do nothing or speak of himself - the Father provided all he needed. The name of Jesus carries the same authority of his God so there is no real need to follow the instruction mentioned in Matt 28:19. Perhaps that is the best reasonable explanation - that no one ever used this supposed baptismal formula in the entire NT.
As the OP has correctly noted in the recent edit, there is nothing to force an understanding that the titles of Holy Spirit and Son are somehow equal to God as distinct entities of a Godhead. This has little to do with the main Q regarding an apparent 'contradiction' - better called a paradox as the two passages regarding the instruction to be baptised and the practise of baptising in Jesus' name only are not expressly at odds with each other.
The practise however reveals an important distinction that dismisses any particular importance of the 3 titles in this process of baptism. To invite deeper speculation is to also invite conjecture. We are warned against adding to the words and truth God has provided through His son and the Apostles to the fledgling church.
For a longer study on this matter from which some of this answer is derived.