I recently wrote an introduction to perf for my scientific computing colleagues, maybe it can be useful to you? It is a bit focused on compute performance, though, whereas for your use case I think you may want to focus more on system-wide analysis (IO, syscalls, mutexes...). For that, I can recommend Brendan Gregg's awesome website.
EDIT: Also, for instructions on using perf with Rust projects, see my posts in Profilers and how to interpret results on recursive functions - #2 by HadrienG .