You might want to consider rephrasing this. I think "however" should be a brand new sentence joined with the next sentence. Something like (warning: I'm not the best writer):
Although rustfmt formats code automatically, this tool will only be responsible for checking whether a .rs file is formatted correctly since the bot will not be changing any code...

When linking a single word, the backticks aren't necessary.

The .rs part should use a :file: role:

:file:`.rs`


I'd also say "Rust-formatted code".

Let's use the :program: role for rustfmt.

Since we're linking, it doesn't seem necessary to say where the docs are found. Let's say:

To learn more, see the documentation on `installing Rust`_ and `installing rustfmt`_.

Ship It!

Ship It!