Personally, I'd recommend learning C to learn about the basics of memory management in higher level languages in general. It is simpler than Rust and is very transparent, making it easier to grok the concepts before moving on to something like the borrow checker, further more, it will actually make the motivations for the borrow checker and what it does to help clear. Same goes for other memory management solutions, gc, reference counting, etc. So much of what we do is still bound to a deeply entrenched model that C established.

Ultimately we are all still just writing nicer versions of C. The fundamental model of pretty much all high level languages remains the same. You can still explain and think about the vast majority of memory related goings-on in a program as using the basic abstraction of the pointer and contiguous arrays of bytes. Even languages that have different paradigms, be they functional, logical, or object oriented can be described in terms of pointers--one easy way to understand pretty much every other programming language paradigm is basically just to ask "how would I implement this using pointers?". It's a shared history and approach to computing we have yet to move on from.