Thank you very much for the question and my apologies for the delayed response!
I think the reason why there is a lack of commentary on Matthias, specifically, is because we sadly don't know much about him. There are no other mentions of him in the NT, and references to him outside the Bible are dubious or obviously confused.
Now, there are a lot of commentary about the replacement of Judas in general, but I'm not sure how much definite we can say about it. As you've mentioned, some have suggested that Paul was intended as the twelfth. While possible, I personally find the view uncharitable, because in the case of Paul and Barnabas, they were commissioned by the Holy Spirit to the Gentiles (Acts 9:15; Acts 13:1-3; Acts 22:21), whereas the twelve were specifically commissioned for Israel (Galatians 2:9), so that the Gospel came to the house of Israel first, then to the Gentiles, which is one of the core themes of Acts and throughout the NT.
As for other candidates, James the brother of our Lord evidently didn't receive Jesus as the Messiah during His ministry (John 7:5), but thanks be to God, he was granted repentance and even became the head of the church of Israel, and with Peter and John are called "pillars" of the Church (1 Corinthians 15:3-11; Galatians 2:9).
However, neither Paul nor James fit the requirements for the office of the twelve laid down in Acts 1, which expresses that the replacement had to be a close follower of Jesus from the beginning, from the baptism of John until the ascension. Now, we don't know where this requirement comes from other than that it is a prophecy by the Holy Spirit, so I think we'll do well to receive it as such. And we don't know how many men were technically eligible for this office, but the Church saw it fit to suggest two candidates (the fact that there were only two, contrary to some commentaries, suggests to me that there were literally only two eligible), and they then cast lots according to the OT practice, and Matthias was chosen.
It may be helpful to consider that there is no rebuke, sad consequence, or any negative writing about the choosing of Matthias in the Biblical account itself. Beyond this, there are perhaps three things that may be good to reflect on:
(1) The Holy Spirit is always given and never fully possessed. We always receive God's gift of the Holy Spirit, who works in our minds and hearts, conforming us into the image of our Lord Jesus Christ. He comes to us in different ways and equips us with different gifts for different vocations. The apostles already had the gift of the Holy Spirit, even before Pentecost, because Jesus breathed on them after the resurrection in John 20:19-23. So, it's in accordance with the Holy Spirit indwelling in Peter and the other apostles, all the 120, and in the written Word that's quoted, that the need for a replacement is brought forth. So, at least my understanding is that the better reading is not that Peter is anxious, but that the Holy Spirit worked through His Church.
(2) The outpouring of the Holy Spirit on Pentecost, from the perspective of the apostles, has to do with the gift of charisma, spiritual gifts. And this was given to Matthias, thereby showing God's approval.
(3) God calls prophets and apostles directly, but the way He calls servants to the pastoral office is through His Church. I think we can see Matthias as a kind of a bridge, because he was undoubtedly called by Jesus during His ministry, otherwise he wouldn't fit the requirements for the apostolic office, but he was also chosen by the Holy Spirit through the Church, which is the same way all pastors are chosen to serve. So, this is to say that the Church choosing a man to serve is not sinful, but in fact good and commanded by God.
In brief, I think the natural reading is simply that Judas fell away, but there were two candidates eligible to replace him, and that this was in accordance with God's Word. And then we do see that God does indeed grant Matthias the gift of the Holy Spirit on Pentecost, affirming that He is chosen by God to serve Him. And though we don't know much, if anything, about Matthias' life and ministry, we can be certain that he proclaimed Christ and helped lay a good foundation for us to stand on, so thanks be to God!
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