There's probably a similar amount of code in the execution path, but the Rust ecosystem reliance on dependencies means that you're pulling in vast amounts of code that doesn't make it to your final application.

A C++ library author is much more likely to just implement a small feature themselves rather than look for another 3rd party library for it. Adding dependencies to your library is a more involved and manual process, so most authors would do it very selectively.

Saying that - a C++ library might depend on Boost and its 14 million LOC. Obviously it's not all being included in the final binary.