The O'Reilly book on sed & awk is available online for free from various sources (I grabbed a rar archive of it from somewhere).
https://freecomputerbooks.com/The-Unix-CD-Bookshelf-Version-...
I referred here to the following definition:
"2.4 Other Language-Related Specifications POSIX.1-2017 is currently specified in terms of the shell command language and ISO C. Bindings to other programming languages are being developed."
But, you are definitely right that some of the tools, defined as standard "utilities", such as AWK, also have their own language. Although, it is only defined in the "utilities" section, https://pubs.opengroup.org/onlinepubs/9699919799/utilities/a... However, "sh" is also defined under "utilities", although it has an extensive language specification that is provided as a separate document.
AWK is also defined in the standard.
Yes, subtleties are lost here.