In context, he's referring to the Jewish scriptures with which Timothy had been taught from childhood. I'm not entirely sure just which books Timothy would have considered canonical, but I believe there's a good chance that the LXX including what came to be called "deuterocanonical books" were part of that corpus. We can't be 100% sure of the exact bounds of the canon of Scripture at the time this epistle was written. Clearly, Timothy was meant to infer from his own situation, just which Scriptures were being referred to.
If we take Paul's words in a categorical sense, that is, "All writings that are within the category of God-breathed Scripture," it's broad enough to include the entire canon of both the Old Testament (no definitive canon of which was formally adopted until the time of the Reformation) and the New Testament (the canon of which wasn't formally and universally accepted until about the 4th century).
Still, at the time this was written, I believe the best explanation is that Paul was referring to the Jewish (OT) scriptures, which were able to prepare him to receive and understand the Gospel of Jesus Christ by faith.
Notice what else he says in his letters, though. He tells Timothy of the kinds of people can be entrusted with the message that he (Paul) is passing on to them.
"21 Therefore, if anyone cleanses himself from what is dishonorable, he will be a vessel for honorable use, set apart as holy, useful to the master of the house, ready for every good work. 22 So flee youthful passions and pursue righteousness, faith, love, and peace, along with those who call on the Lord from a pure heart." (2 Tim 2)
"14 But as for you, continue in what you have learned and have firmly believed, knowing
from whom you learned it 15 and how from childhood you have been acquainted with the sacred writings, which are able to make you wise for salvation through faith in Christ Jesus."
This would seem to be his grandmother and mother, mentioned in Ch.1. The scriptures are sufficient, but they must be properly learned and understood. This is the task of teachers.
And, the entire context of both epistles to Timothy is basically Paul's instructions for how to identify and appoint faithful elders and deacons who can shepherd the churches and carry on the teaching and service begun by the apostles (in this case, at least, it's Paul himself).
As early as Ignatius of Antioch, we see a letter written to the church in Ephesus likely only a few generations after Timothy himself had been a bishop...admonishing his readers to continue in submission to their bishops, elders and deacons.
Clearly, the sufficiency of the Scriptures is not at odds with the authority of the Church's ordained ministry. It is the task of the entire Church, led by those ordained to that ministry through the laying on of hands, to safeguard the entire tradition received from the Apostles, within which the Scriptures can be properly understood and lived out.
I believe you've also sidestepped my entire line of questioning to you.