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 spell specifies you turn into gray dust. Unfortunately gray dust has no listed stat block.
Luckily it is mentioned in "Tales from the Yawning Portal", "The floor of this room is covered with a layer of fine gray dust and ash, three inches deep."
Based on the rest of the description you are restricted to the room in which you turned to dust and the only action you may take is casting " Minor Illusion", with the added restriction of all illusions must be humanoid.
Disintegrate also specifies the creature can only be brought back to life with a true resurrection or wish spell. Which most certainly means it is indeed dead, otherwise, why mention bringing it back to life?