Dependencies have nothing to do with low-level vs. high-level but just package management, how well the language composes, and how rich the standard library is. Are assumptions in package A able to affect package B. In C that's almost impossible to avoid, because different people have different ideas about how long their objects live.
Having a rich standard library isn't just a pure positive. More code means more maintenance.
That being said Rust is definitely a much higher level language than either C or Zig. The availability of `Arc` and `Box`, the existence and reliance on `drop`, and all of `async` are things that just wouldn't exist in Zig and allow Rust programmers to think at higher levels of abstraction when it comes to memory management.
> Having a rich standard library isn't just a pure positive. More code means more maintenance.
I would argue it's much worse to rely on packages that are not in the standard library since its harder to gain trust on maintenance and quality of the code you rely on. I do agree that more code is almost always just more of a burden though.