Proper asynchronous programming is not something that's hype. In fact, it's something that is quickly disappearing from most I/O-bound code.
Low-level asynchronous I/O (think epoll, kqueue, IOCP) was popularly implemented by many high-performance servers in the early 2000s, often as response to the C10k problems. It's really Nginx, Haproxy, Lighttpd, libevent (and later libev and libuv) which popularized this programming style in systems programming.

It's worth noting that during the 1990s, multi-threaded programming did not completely dominate as the model for network servers. I believe it was mostly due to multi-threading support was uneven across the different UNIX flavours of the day, but regardless of the cause, some popular servers (mostly notably Apache httpd) started out as multi-process based, using a pool forks the same way you'd use a thread pool. Other servers were written using the 1990s incarnation of asynchronous programming, essentially using select() or poll() (or WSAWaitForMultipleEvents on windows). From the programmer's perspective, these act mostly the same epoll, but are just less efficient.

It is during that time that the C10k problem and its asynchronous solution was experiencing its peak hype cycle that high-level languages got interested in the game, and implemented asynchronous I/O with callbacks. I believe it started with Python and Twisted, but node was the poster-child. OS-level threads were either not supported by the language (Node.js) or severely encumbered by having a GIL (Python). Green threads or coroutines would have probably been a better fit for this languages, but if you're just writing a library or a runtime for a language you don't control, that's harder (of course, gevent in Python went and manage to do that anyway).

By the time async/await came to Javascript, this wasn't part of a hype. Javascript has already widely adopted callbacks and then promises as a bottom-up, library oriented solution. Most I/O APIs were promise-based. Even if ES6 added go-like coroutines, all the APIs you had were already accepting a callback or returning a promise. You'd still had to do something like "await(myApi())" every time you're calling that API, not to mention having to introduce synchronization primitives to the language and watching code that never had to care about synchronization before break.

Async/await by itself, is not really asynchronous programming. Behind the scenes, it is implemented asynchronously (just the same as I/O in goroutines is!), but the programmer is writing code that looks linear and synchronous. The real trend nowadays is to eschew synchronous I/O and hide the complexity of asynchronous I/O behind synchronous-looking code. Explicitly asynchronous programming (like callbacks or non-awaitable promises) is just as trendy as Ruby on Rails or flip phones, that is - yeah, sure, it was fairly trendy back in the 2005.

Nowadays you've got two popular M:N thread models for running multiple synchronous tasks which perform asynchronous I/O behind the scenes: The green thread model (Go, Java's Virtual Threads) and the state machine transformation model (a.k.a. async/await). If you think the async/await model is inferior to the green thread model used by Go, that's a different story. I think each has its own pros and cons, but claiming that only async/await receives hype is untrue. The green threading model receives a fair share of its own hype ("Which color is your function"), and its usually the proponents of the green threading model who claim that their model is strictly superior while the other model has no merit at all, and not otherwise.

If you go back to Rust, Rust definitely tried the green threads model, as many people have already said. It had to abandon it. Go is not to be a full-spectrum systems language, and can get along pretty well with being garbage collected and running its own scheduler. Rust has to run on some environments and contexts where you just can't do that. Rust is also very sensitive to overhead introduced by features (that's the entire "zero-cost abstraction" theme), and it does not shy away from adding some complexity in exchange of performance. Otherwise why won't it just do away with lifetimes altogether?

While I concur the callbacks hype in JS was probably misguided (although understandable), I find it hard to believe that the decision to use async/await in Rust was based on hype.