As you indicate, γραφαῖς (graphais) generically means writings, but in the NT it most often refers to those writings, the Scriptures, which are recognized as authoritative, truthful, God-breathed (2 Tim. 3:16), and prophetically-delivered (2 Pet. 1:20–21). In the NT, this term most often refers to OT writings; but (contra BDAG), it is also used to refer to NT writings (1 Tim. 5:17–18; 2 Pet. 3:15–17). Further, in 2 Timothy 3:15, Paul uses "sacred writings" (ESV) to distinguish between OT writings and NT writings, as he shifts from speaking of the OT writings of Timothy's childhood to inclusively speaking of the NT writings ("All Scripture"), which were profitable for training, making complete, and equipping the [Christian] "man of God."1
From within this framework, is there an explanation for how Apollos might have only known of the baptism of John? Indeed there is, if Apollos had been instructed from one of the Gospels, without an awareness of the events of Pentecost which had not yet been published (i.e., in Acts). Elsewhere (here, here, and here), I have argued that Matthew was published well before this encounter in Ephesus; therefore, we can easily explain Apollos' limited knowledge. Hence, to directly answer the OP question, the passage's Scripture reference is referring to "something else"; namely, a Gospel, such as Matthew.
The phrase which follows Acts 18:24 is also pertinent, as the phrase can be understood as elaborating on the Scriptures which were in view; namely, Scriptures which "instructed in the way of the Lord." (Elsewhere, we've established that these kinds of references to "Lord" have Jesus in view.) This echoes Paul's expectation of the role of Scripture, per 2 Timothy 3:16–17, as referenced above.
24 Now a Jew named Apollos, a native of Alexandria, came to Ephesus. He was an eloquent man, competent in the Scriptures. 25 He had been instructed in the way of the Lord. And being fervent in spirit, he spoke and taught accurately the things concerning Jesus, though he knew only the baptism of John. (Acts 18:24–25 ESV)
The OP asked a follow-up question, "is it possible to read this to mean that he was a skilled writer?" Yes, this is a fair speculation, given that he was eloquent and competent in the Scriptures. The best orators of the day taught that orators should be well read and written. For example, Cicero offered this advice:
Write as much as possible. The pen is the best and most eminent author and teacher of eloquence … all the thoughts and expressions … needs flow up in succession to the point of our pen … the actual marshalling and arrangement of words is made perfect in the course of writing, in a rhythm and measure proper to oratory as distinct from poetry.2
Quintilian, in his Institutes of Oratory, also
shows the close relationship between reading, writing, and oratory. In his introduction he asserts that a student may have a good voice, endurance and grace, but, “they are of no profit in themselves unless cultivated by skillful teaching, persistent study and continuous and extensive practice in writing, reading and speaking.”3
1 Swinson does an excellent job of addressing this issue. L. Timothy Swinson, What Is Scripture? Paul’s Use of Graphe in the Letters to Timothy (Eugene, OR: Wipf & Stock, 2014).
2 Cicero, De or. 1.3, 1.32–33. Also, Cicero, De or. 2.84, 3.44. More broadly, the orator must also devote himself to constant reading and writing, “for the genuine orator must have investigated and heard and read and discussed and handled and debated the whole of the contents of the life of mankind, inasmuch as that is the field of the orator’s activity, the subject matter of his study.” Cicero, De or. 3.14. Also, Cicero, De or. 1.21. As cited in Daniel B. Moore, A Trustworthy Gospel: Arguments for an Early Date for Matthew’s Gospel (Eugene, OR: Wipf and Stock, 2024), 100.
3 Quintilian, Inst. 1.0.1; 1.0.27. As cited in Moore, A Trustworthy Gospel, 102.