Use of libraries may be more common in rust than c because of many possible factors:
1. Rust's standard library is large and contains data structures. People are good at centralizing on one thing if it's the standard one, if there are 10 competing string libraries, people might say "ah well, let's write our own". That also sometime means using one dependency will pull in others (e.g. in C you might want someone's regex library, but it might be incompatible with your string library because it uses a different one. A stdlib helps ensure libraries have a standard set of types to talk about, and C barely has that).
2. Rust's package manager (cargo) and registry (crates.io) are really good and making finding and adding dependencies much easier. If I want to add a random library on github to my rust project, it's 1 line in my Cargo.toml (whether it's on crates or not). In C, I have to figure out if they're using cmake, meson, autotools, or any of a dozen other things, and possibly vendor the code into a third_party folder, and possible spend several hours hacking on my build system to link against it.
3. Rust's community has made an effort to standardize on certain crates and include their use. See the rustlang nursery. The closest to this in C is stuff like the gnulib I think, which is an ancient effort pushing garbage code that suffers from the lack of good dependency management severely. I know of no recent similar efforts for C.
4. Rust has generics and a better type system in general which makes it much easier to implement generally usable libraries.
It's important to remember that C also predates the internet, and many c codebases also predate modern package management. Legacy practices have a habit of propagating themselves.
1. Rust's standard library is large and contains data structures. People are good at centralizing on one thing if it's the standard one, if there are 10 competing string libraries, people might say "ah well, let's write our own". That also sometime means using one dependency will pull in others (e.g. in C you might want someone's regex library, but it might be incompatible with your string library because it uses a different one. A stdlib helps ensure libraries have a standard set of types to talk about, and C barely has that).
2. Rust's package manager (cargo) and registry (crates.io) are really good and making finding and adding dependencies much easier. If I want to add a random library on github to my rust project, it's 1 line in my Cargo.toml (whether it's on crates or not). In C, I have to figure out if they're using cmake, meson, autotools, or any of a dozen other things, and possibly vendor the code into a third_party folder, and possible spend several hours hacking on my build system to link against it.
3. Rust's community has made an effort to standardize on certain crates and include their use. See the rustlang nursery. The closest to this in C is stuff like the gnulib I think, which is an ancient effort pushing garbage code that suffers from the lack of good dependency management severely. I know of no recent similar efforts for C.
4. Rust has generics and a better type system in general which makes it much easier to implement generally usable libraries.
It's important to remember that C also predates the internet, and many c codebases also predate modern package management. Legacy practices have a habit of propagating themselves.