Rust does not in general have an order of magnitude advantage over Go. 2 or 3 would be closer, and that's with some nontrivial attention paid to optimization, not "you write Rust and it's automatically always faster".
Super high-end stuff can outclass Go by that much, like if you're seriously using DPDK or something, and in those cases I strongly recommend Rust over Go. There some other noches like that. But in general, it's not a factor of magnitude.
It really depends. I agree it's not always an entire order of magnitude didn't mean to paint that picture for passerbys who don't know better. Not trying to touch the "this lang vs that lang performance" conversation with a ten foot pole...
10x improvement over Go is a reasonable expectation, in a limited set of environments, generally at a scale where you're looking at using every last bit of a 32-core or 64-core machine and doing a lot of memory work. You should also expect to be spending a lot of time optimizing that Rust to get there. But when you need that level of performance, you also basically made a mistake starting with Go in the first place.
However, by far the bigger problem is people thinking their little web service serving out 5 requests a second requires that level of optimization when in fact even a Go implementation will use <1% of the CPU and no other resources to speak of. Dynamic scripting languages, IMHO, have skewed a lot of people's performance views. Go is already more power than most problems need, in terms of raw performance, and it's only a sliver, a niche where that's the difference between a Go vs. Rust choice.
It's a delicate understanding, but an important one for a professional.
I would not suggest using DPDK with Rust, unless you want to write a lot of stuff for yourself and wrangle with some tricky `unsafe` code. Sticking to C or C++ will make your life a lot easier.
Super high-end stuff can outclass Go by that much, like if you're seriously using DPDK or something, and in those cases I strongly recommend Rust over Go. There some other noches like that. But in general, it's not a factor of magnitude.