These versions are more along the lines of a literal translation for Acts 20:28 even though the word for "son" is not actually in the verse. It's implied through the context and grammar. This is what the Greek actually says because God doesn't have blood. It's because Jesus and God aren't the same person.
For example, the Lamb purchase for God (the action is moving from one location to another location) with his blood.
Revelation 5
9And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast r
edeemed us to God by thy blood out of every kindred, and tongue, and people, and nation;
Contemporary English Version
Look after yourselves and everyone the Holy Spirit has placed in your care. Be like shepherds to God's church. It is the flock he bought with
the blood of his own Son.
Good News Translation
So keep watch over yourselves and over all the flock which the Holy Spirit has placed in your care. Be shepherds of the church of God, which he made
his own through the blood of his Son.
NET Bible
Watch out for yourselves and for all the flock of which the Holy Spirit has made you overseers, to shepherd the church of God that he obtained
with the blood of his own Son.
Darby Bible Translation
Take heed therefore to yourselves, and to all the flock, wherein the Holy Spirit has set you as overseers, to shepherd the assembly of God, which he
has purchased with the blood of his own.
I hope that helps! Let me know if you're cleared up now. Next fallacy.