Rust also has automatic formatting [0]
I don't think the tooling is why there is a perceived "Go vs Rust" culture, I think that's due to (somewhat) overlapping use cases, or more probably that they were developed and came out around roughly the same time. There really doesn't need to be a "Go vs Rust" culture though.
I think it should be obvious to most people that Go had a big influence on Rust and other modern languages for the benefit of having unified tooling, formatter, linter, etc.