There are multiple standards for C. C23 does not replace C17, or C11, or C99, or even C89. Maybe something should replace C89, but that's another discussion. I'd vote for C99 as a minimum target and prefer C11.
Just as you yourself described, one can absolutely target a platform from scratch with C99, Forth, Lua, a Pascal, a modernish Basic dialect, or some form of Lisp without building the largest, most modern compiler first. Once you have a compiler or even an interpreter for any of those, one can use it to create a compiler for something bigger and more modern. In fact, that's precisely where C was originally targeted - as a portable bootstrap language to various hardware platforms.
On the other hand, one can also target a new platform via LLVM. Both options have their merits and drawbacks.
Just as you yourself described, one can absolutely target a platform from scratch with C99, Forth, Lua, a Pascal, a modernish Basic dialect, or some form of Lisp without building the largest, most modern compiler first. Once you have a compiler or even an interpreter for any of those, one can use it to create a compiler for something bigger and more modern. In fact, that's precisely where C was originally targeted - as a portable bootstrap language to various hardware platforms.
On the other hand, one can also target a new platform via LLVM. Both options have their merits and drawbacks.