Why does that have to be global? You can still pass it around. If you don't want to clobber registers, you can still put it in a struct. I don't imagine you are trying to avoid the overhead of dereferencing a pointer.
I think a better example might be logging. How is this typically solved in Rust? Do you have to pass a Logger reference to every function that potentially wants to log something? (In C++ you would typically have functions/macros that operate on a global logger instance.)
In Rust you typically use the "log" crate, which also has a global logger instance [0]. There is also "tracing" which uses thread local storage.
As another comment said, global state is allowed. It just has to be proven thread-safe via Rust's Send and Sync traits, and 'static lifetime. I've used things like LazyLock and ArcSwap to achieve this in the past.
I wonder what the advantage of passing it around is when it makes the argument list longer. The only advantage that I can see is that it emphasizes that this function does something with cache.
