As I stated, it's possibly from the first century, as early as AD 50. It's only catholic in the sense that it is of the universal Church.The Didache is a second century CATHOLIC document.
I'm not sure why you quoted all those verses when they very much agree with the doctrine of the Trinity. To use them as you do is to fallaciously beg the question. This verse in particular is telling, since you avoided emphasizing of "the Spirit of Christ":Romans 8:9
You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ.
Rom 8:9 You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him.
Note what Paul first states positively to believers--that if "the Spirit of God dwells in" them, they are "in the Spirit." However, he then states the same thing negatively--"Anyone who does not have the Spirit of Christ," that is, if the Spirit of Christ does not dwell in them, then they do "not belong to him." Paul is unequivocally stating that "the Spirit," "the Spirit of God," and "the Spirit of Christ" are all one and the same.
This is how Peter refers to the Holy Spirit in the OT:
1Pe 1:11 inquiring what person or time the Spirit of Christ in them was indicating when he predicted the sufferings of Christ and the subsequent glories.
Also here:
Act 16:6 And they went through the region of Phrygia and Galatia, having been forbidden by the Holy Spirit to speak the word in Asia.
Act 16:7 And when they had come up to Mysia, they attempted to go into Bithynia, but the Spirit of Jesus did not allow them.
Php 1:19 for I know that through your prayers and the help of the Spirit of Jesus Christ this will turn out for my deliverance,
And:
Gal 4:6 And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!”
In addition to Rom 8:9, compare Gal 4:6 with:
Joh 14:17 even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you and will be in you.
(All ESV.)
It is the Holy Spirit, the Spirit of God and Spirit of Christ and Spirit of his Son, who indwells all believers. It cannot be said, then, the Holy Spirit is a title for the Father.