Adding a single unused function should no effect on runtime performance. The compiler removes dead code during compilation, and there’s no concept at runtime anyway of “creating a function” since it’s just a compile-time construct to group reusable code (generally speaking - yes the pedants will be right when they say functions appear in the compiled output, to some extent).
Anyway, this can all be tested on Godbolt anyway if you want to verify yourself. Make a function with and without a nested unused function and check the output.
The “‘modern’ development stack” we used at my school when I was in a CS program was C++98 or something, compiled using gcc directly. This was in the last decade. It technically wasn’t C!
But we did use C in my computer engineering classes so I guess they technically did teach it. I feel very fortunate that I haven’t needed to use it since then.