Giving in the end you are comparing, for me at least Rust is more in the family of languages like C++.
Very powerful, fast and close to the metal, but with uglier* syntax and not as productive as the next family of languages. Which are:
Java, C# and Swift (unlike C++ and Rust) for me are pointing into solving a very hot spot of programming, with the balance of power, being more pleasant to program in and feeling more productive.
Your code will be almost as fast as a C++ program, but you dont need to feel (that much) miserable writing stuff into it. (And i say this as someone that likes C++, but knows its not the most productive and pleasant experience)
It remedy some pain points of programming, that in my point of view at least, Rust didnt addressed the same sweet spot as Swift does.
Theres also some good things about Swift right in the corner, that is support to C++ bindings and a more fine-grained control of memory.
Once the memory ownership changes, than we will also be able to consider Swift for the same things as C, C++, Rust and Zig can right now.
Also i would say that dinamic calls while embedding script languages and function builders are very strong points that the language is becoming more powerful with each release.
Also some things like binary stability that Swift have that Rust doesnt are thing to take into account for, giving there are a lot of cases were shipping just the binaries and know they will still work is something very important for projects that cant afford to be open source.
I would consider to use Rust whenever C++ would also fit, but if i can use Swift i would not consider using Rust, because at least for me is a much better language to code.
I think people from the Rust community dont need to fear, because Rust have a strong community right now, and in that particular topic, is Swift that need to catch up and shake up this feeling of being a "apple owned language".
So i dont think they are aiming for the same thing, and therefore they dont need to be compared in a us vs. them basis, giving you can code on both, and i think it could be great if you do it.
Theres a false adage that you need to pick just one language, and having used a lot of languages and platforms over the years, im pretty happy now that i know that such thing doesnt exist.
You are better picking from 2 to 3 languages and use them according the goals of what you are building.
For me, my three languages are: C++, Swift and Python.
C++ for hardcore stuff, Swift for everything that a language like Java or C# could be considered and Python for the more relaxed (and now also expert) stuff.
You can replace Python with Ruby, Lua, etc..
replace Swift with C#, Kotlin, Java, Go, Scala, etc..
and replace C++ with Rust, Zig or C.
But if you mix the families, i say you will have a hard time using Python or C++ in the wrong places.
And this rule is also valid for Rust unfortunately.
* Note: i know this is subjective and a lot of people would find it more beautiful than Swift instead. Its ok and even good that we dont all have the same tastes.