Most of the “automation” work that I do involves parsing data with regex, restructuring the data, converting the data into a modeled format and transforming something with that data.
These are the highlights of rust - regexes (the regex library that powers ripgrep), serialization/deserialization (serde, nom, pest, capnproto, etc), data manipulation (too many. perhaps apache arrow deserves a mention), etc. The language is designed for this sort of stuff.
Has anyone used Rust for network automation tools?
I'm in the same boat as you. I use python to manage an LXD cluster. I didn't choose Rust because Python has an API binding, but Rust didn't. It wouldn't have been too hard, considering that the API is mostly just JSON.
With familiarity, can Rust’s intuitiveness match Python’s “from idea to deployment” speed?
Unfortunately no! (in my personal experience). I have been using Rust for a decade (since before 1.0) and am more or less comfortable with it. I no longer fight with the compiler as most beginners do. Still, the compiler complains a lot and you have to think about why. This is not bad, IMO - all that thinking make you design better programs. There is always a sweet satisfaction of writing excellent code when you finish a Rust program - probably the reason why Rust developers love it so much. But you have to sacrifice some speed for that.
Intuitiveness is also subjective. My introduction to programming and computers was from the hardware side - from ALUs, DRAM, hardware pipelining etc. Rust's rules are very well defined, but is obscurely related to real problems you encounter in the hardware. In other words, Rust rules look confusing at first, but it makes sense once you see the error messages. You know what problem could have happened on the hardware if Rust didn't stop you. It's as if Rust's simple rules magically cover the problems you dread on the hardware.
All this means that Rust is easy to grasp for people who are already using C - OS, game engine, web engine and embedded system developers. For others who are mostly used to GC languages, it's an uphill battle with the compiler, until some day it clicks somehow. With Rust, it's very important to start right away with the (c lang) memory model and Rust's aliasing rules.
Or should I only learn Rust if I intend to create applications that need tight performance?
I wouldn't say no to learning a new language. But I always recommend a few languages because they introduce a radically different idea. Rust is one of them. My rant above probably gave you an idea why I would recommend Rust. The first is that Rust forces you to design programs properly - even though the rules are meant only to enforce memory safety. Second is that Rust gets you very close to the soul of the hardware. Python and even Go has some opaque layers in between you and the hardware. With Rust, you'll get every opportunity to get the best the hardware can offer. You get the same in C and C++ - but they also allow you to screw up.
I use Rust for even trivial tasks where a shell script would suffice. Besides the language features, Rust has excellent tooling and a rapidly growing library ecosystem. In many ways, it's easier to package Rust programs than Python ones. So Rust will work for your use case. But if development speed is more important to you than performance, then Go (similar to Python), Nim (much more similar to Python) and Zig are probably better choices. Repeating something here - Go is designed for the web. Numerous web backends are already on Go. And almost the entirety of Kubernetes is written in Go.