Oluwarotimi Paul Adebayo has produced an article addressing the referent of γραφή in its two occurrences in the Letters to Timothy:

Adebayo, Oluwarotimi Paul. “The Politics of the Term γραφή in the Pastoral Epistles.” Scriptura 119.2 (2020): 1–11.

The article may be found online here.

Abstract: “The understanding of the term Scripture in early Christianity is best described as an evolving concept that can be categorised into various stages. This can best be seen in the most popular Greek term the NT uses in designating Scripture, γραφή and its cognates. Γραφή was used 50 times in the NT to represent Scripture, and in each of these instances, it refers to more than just a mere writing which is what the term originally meant in Greek prior to the NT’s consistent use of it as a technical term for sacred writing.
“This study attempts to reflect briefly on (part of) the evolution γραφή underwent on the pages of the NT especially within the Pastoral Epistles (PE) – a product of the early second century CE. This study bears in mind that the recognition of books as Scripture is not a series of clearly defined steps, but rather a long and complicated process involving creativity and powerplay. This study therefore serves to enhance a more accurate understanding of the transition the concept of Scripture in the PE, most especially pertaining to the use of the term γραφή.
“The question regarding the scope of the term γραφή in the NT and especially in the PE is open to debate – especially the use of the two different words, ἱερὰ γράμματα and γραφή for Scripture in 2 Tim. 3:15–16. So is the reference to Jesus’ words as Scripture in 1 Tim. 5:18. These have raised questions of a possible shift in the PE’s understanding of γραφή. “Findings from this research include the extensive use of γραφή in the PE to accommodate more than just the Jewish Scripture, as it has evolved to include emerging earlier writings of the NT; the author of the PE was creative in adopting and adapting to a new understanding of sacred writings which serves the context of his time.
“This unveils the influence a community exerts on recognition of authoritative Scripture while teasing out the politics intertwined in the recognition of Scripture and the identity of a people, as this later became the path to canonicity of Scripture.”