At this point in my experience, if I want to learn a language, I write something "easy" in the language that I want to write for my enjoyment.
For example, when I was between jobs I wrote a personal blog engine in NodeJS so I could get up to speed in modern Javascript and the node ecosystem: https://github.com/GWBasic/z3
"Silly exercises" implies a programming exercise that has little point outside of instructing a basic concept: The kind of exercises I did in high school when I learned C are an example; there was no outside purpose to the code itself. IE, there's no tangible use to the code when it's complete.
What I did 3 years ago was write a small program in Rust that opens links listed in a text file. (I've written many versions of this program over the last 18 years, mostly for self-education.) When I first wrote the program, it was mostly copy & paste, but it compiled even though I didn't understand most of it.
Last night I decided that I was going to recompile it on Windows as my first exercise. I had to change the "open a link" library because it only compiled on Mac, which required changing some code: https://github.com/GWBasic/open_links
Now I'm going to try porting my in-browser Javascript in Z3 to Rust + WebAssembly. Let's see how far I can get!
Even ignoring that, it's a matter of big picture.
If learning Rust is only for this project, or only to be "quickly proficient in a new language", then I don't think it fits the specific case. The may be alternatives; I don't have experience (somebody else can surely advice better) something like C++ with smart pointers or memory safe D, I guess, could fit.
In the big picture of a career, or even in the context of a single company, spending 40/80 hours to be proficient in a language is essentially an insignificant time.