C has the same problem, but it lacks a common package manager like other languages do. Just because you need to clone git submodules or run package manager commands (hope you're on a supported OS version!) doesn't mean C doesn't have package manager issues.
C projects avoiding dependencies entirely just end up reimplementing work. You can do that in any language.
But is optional. For this kind of project, is logical to adopt something like the tiger battle ethos and own all the code and have no external deps (or vendor them). Even do
your own std if wanna.
Is hard work? But is not that different from what you see in certain C projects that neither use external deps
The lack of dependency hell is a bit of an illusion when it comes to C. What other languages solve via library most C projects will reimplement themselves, which of course increases the chance for bugs.
Then don't? In C you would just implement everything yourself, so go do that in Rust if you don't want dependencies.
In C I've seen more half-baked json implementations than I can count on my fingers because using dependencies is too cumbersome in that ecosystem and people just write it themselves but most of the time with more bugs.
If you care about not having any dependencies, then choosing dependencies that themselves don't have many dependencies should be going into the ones that you choose.