I've been programming in Odin for a few months now, and I've come to actually like this choice.
I still use the occasional dependency, and installing it is even easier than with a package manager!
I download a repo as zip from github, extract it in my project, and voilà, it's ready to use. No compilation, transpilation, peer dependencies, locking versions, etc.
Another positive of this approach is that I can now easily read the dependency source code and if needed modify it, as it's become a part of my project, not some transpiled and minified version of that code sitting in an unversioned folder.
Overall, in Odin I use dependencies much more sparingly than when I work with JS. The reason is that the core and vendor packages of the language already include a surprising amount of things you'd normally reach npm/cargo for. Need linear algebra primitives? Specialized data structures like a priority queue? SDL2? stbi? It's all included in the language (and so much more), ready to use.
I've come to realize that more often than not it's fine to reinvent the wheel to solve your specific problem rather than relying on a generalized (and thus unoptimized) 3rd party library.