The term "speech repertoire" actually came from phonetics research in the 1950s. The use of the term "repertoire" in music appears to be relevant, but each "piece of music" was equated to various phonetic properties, defined by the study.
This was later adapted to other linguistic fields, e.g. developmental neurolinguistics and sociolinguistics. Just as in music, the use of "repertoire" implies a range, and various different items. However, unlike in musicology where the "pieces" are quite well-defined, in sociolinguistics the "speech varieties" in one's "speech repertoire" are generally defined by the authors of the study. John Gumperz is credited with introducing it to sociolinguistics, as linguistic / verbal repertoire:
defined as the totality of linguistic forms regularly
employed within the community in the course of socially significant interaction.
The term is widely used in studies about code-switching environments, including natively multilingual ones. The term also seems to have found a niche in describing the acrolect-mesolect-basilect / tformal-informal / rhetorical-communicative axis. Indeed, accents do form varieties that are within the scope of the "repertoire". Gumperz's original example was about the varieties of the Hindi language that a Westerner might need to master in New Delhi, and the pitfalls along the way.
I can also imagine the performative aspect of drama and theatre might require a range of accents to be part of the "repertoire". That would make each accent and each performance one of the "pieces".
In some studies, repertoire-based approaches to sociolinguistics contrast with variationist approaches. This distinction is most obvious when dealing with individual speakers: the repertoire approach requires a lot more data about aspects of the individual's linguistic diversity and linguistic ecosystem.