Rust lets you do nostd (no standard library), it's targetted towards embedded development.
That said, IMO dependency bloat is not a language specific problem, but a library specific problem (essentially how a specific community thinks).
I can't give examples in rust, since I'm new. But for example in Python, I've observed many modern commercially supported libraries (i.e. open source, but with a company behind it) tend to be bloated as they almost always have too many "features", includes stuff like dashboards, authentication, etc, as opposed to open source projects driven by a community.
Bloat is a mindset.