Disclaimer: this is purposefully obtuse.
Other effects in the game which explicitly state they kill you:
Shadows, succubi, massive damage, death saving throws, beholder death ray (notably not even their disintegration ray kills you), power word kill, vampires, mind flayers, night hags, drow inquisitors.
Clearly, if they intended for disintegration to kill you, they'd have said so. Since specific overrides general, and there is no general rule that disintegrated creatures are dead, I rest my case. QED.
The RAW makes a lot of assumptions about the reading comprehension of the reader though. If you want the RAW to hold your hand through understanding basic English, then you're always going to have these problems.
Look, in your opening post, you state "Clearly, if they intended for disintegration to kill you, they’d have said so."
They HAVE said so. Crawford has explicitly clarified this.
Well, regardless of anything, WotC can't prevent this kind of argument by "writing better rules." This isn't the kind of "gotcha" edge case they should need to cover - that's what the DM is for.
Rules lawyers will always appeal to the "the rules don't explicitly state a caveat the one weird edge case I made up that's plainly not intended" as if it's a valid position. You can't build a system this complex and exhaustively cover every take, and the intended mechanism for handling this is that the DM decides if they'll accept such things or not. That depends on your DM and table culture.
As a general piece of advice, this is an extreme level of "the rules don't explicitly say the exact thing I think they should say with the exact wording I demand of them, so therefore my take is RAW". Most DMs would probably not want to keep running a game where this happens regularly. It's exhausting, and they'd rather be getting on with the game, or they'd rather be crafting new NPCs and side-stories. My advice would be to talk things over with your DM away from the table to see what style of game they enjoy before deploying something like this at the table.
You specifically asked for where in RAW it says you can't do this. Cephalotrocity correctly identified the part of RAW that's supposed to do that for you. It's up to you whether you want to accept that or not. It's up to your DM if they want to play with you or not.
Given all this, you asked "where does the RAW say you can't do this" and you've been shown the section that's supposed to do that I don't have much more advice for you - your question has been answered.
I'm going back to drawing silly comics instead.
(my brother in Mystra, we're in a meme community. I'm fucking with you.)
Hmmm
We used to just call it a little bit of light trolling friend, but if you think I'm a douchebag for meming in a meme community I personally think that says more about you.
Unfortunately, there are plenty of people for whom this advice is really needed. I've a couple decades experience running drop-in games and boy do people do this for real. It's a table-wrecker.
Send 'em round to mine!
They've had plenty of time to errata it, they even did a full rules refresh on 2024 and didn't add it to the spell to my knowledge. And Crawford's advice is not official rules, and famously error prone or just bad. Sorry mate, just telling you what the spell says.
Crawford's statement there makes it clear that he believes "being turned to dust" kills you. He believes it's so obvious that he doesn't need to explain it. That's why his statement just takes "you're killed" as a given.
The rules aren't written in such a fashion as to very slowly and patiently explain every possible interpretation to you and hold-your hand to finding the correct one. They assume you have a basic reading comprehension. It's not really WotC's job to fix that if it's a failed assumption.
WotC don't issue errata for stuff like this, because they think the argument is facially stupid. If they issued errata for every facially stupid argument, then the errata document would become so large that it'd be unusable - there's an infinite well of dumb takes that don't require an errata to clean up.
That's the job of your DM.