Rod Ellis' "The Study of Second Language Acquisition" book has a chapter on SCT, you can look at it. Also, Pathan et al.'s (2018) article, "A Critical Review of Vygotsky’s Socio-Cultural Theory in Second Language Acquisition", seems helpful.
Actually, SFL offers a good source of sociolinguistic aspects. Two books are recommended to be consulted. Halliday, M.A.K. ,1978. Language as social semiotic : The social interpretation of language and meaning. Secondly, Halliday, M.A.K. & Hasan, R. 1985. Language, context and text: aspects of language in a social semiotic perspective.
The earlier writings of Late Ruqaiya Hasan , wife of Late M.A.K. Halliday, are also good. For example, on Basil Bernstein's Theory of Social Class. Also, her book : Language and Education: Learning and Teaching in Society, which is the third Volume of her collected works edited by. Jonathan J. Webster.