* If you're going to emulate a writing style, you need to go all in. Study the word selection, cadence, choice of punctuation…go back regularly to ensure you're consistent with it. Once you set up a reader's expectations, anything that doesn't match will stick out and break their immersion. Read it yourself, and then if possible get others to read it too and do the same thing: hopefully they'll see the problems you may have missed.
* Each of the original blog posts had one specific "technical flex" in mind, and they stayed on topic. The one here is not quite clear: it seems like it's "programming on the bare metal", but it does too many things for a result that isn't all that surprising. Ok, you ditch Rust's standard library, and core features of the language…but then you copy paste it back anyways, and after that you link against libc and call printf. The point is to show that you can do better with all your work, not the same.
* At the very end: you are an expert Rust developer, better than your interviewer. You know you're not going to get an offer, but you didn't want one from them anyways. You're certainly not desperate to impress them.
Now that I've read the whole thing, a couple of technical comments:
* You can use -lc on macOS, libSystem will handle it for you.
* The existence of a "frame pointer" is a myth spread by bad programmers. There's no point in touching that register and certainly no need to waste two bytes stashing it on the stack, for goodness sake!