After some time with rust I have found that browsing docs locally is more convenient than searching through online. It took me some time to realise hence sharing it here.
cargo doc --open will open all the current crate docs, but also will generate docs for all dependencies. Hence it generates one big solid documentation resource including all libraries used through whole dependencies tree, search allows to quickly find a cross those libs and nav menu on the left allows to pick for specific dependency.
The only thing it does not include is docs from standard library, though those can be easily generated locally via