Where does the modern canonical version of the Turing machine come from?
Is it due to Sipser? Or Penrose?

Sorry, that made me laugh out loud.  Penrose?

Today's notion of formal language (a language is a set of words or strings) can be traced at least as far back as Frege in the late 1800's and Thue in the early 1900's.  Chomsky's 1956 paper was very influential, and definitely uses the term "language" for a set of strings.

There is also the 1961 paper of Bar-Hillel, Perles, and Shamir.  I would check that.  

This 1963 paper by Evey (https://www.computer.org/csdl/proceedings/afips/1963/5063/00/50630215.pdf ) uses the term "language" in the modern sense in relation to machines.  Perhaps earlier explicit references can be found in the work of Emil Post.