Green’s Dictionary of Slang

z v.

also ze, z-out, z’s, zzz
[z n.1 ]

(US black/teen) to sleep.

[US]Baker et al. CUSS.
[Aus]D. O’Grady A Bottle of Sandwiches 131: Ernie was still zzzzing away.
[US]D. Claerbaut Black Jargon in White America 87: z’sing v. sleeping; napping.
[US]Eble Campus Sl. Mar. 7: z-out – to fall asleep.
[US]Eble Sl. and Sociability 30: In college slang out is the most productive particle: [...] z-out ‘go to sleep.’.

In phrases

z’d out (adj.)

(US teen) unable to wake up properly, still sleepy.

F. Pfeil Goodman 2020 90: Anna went once, must have been three hundred people in the room, half of them z’d out beyond hearing.
J.L. Marshall Flashlight Dream 193: You’re Z’d out, never to return.