They aren’t in different trust zones, because there’s nothing to trust in either of those. The reason for using different passwords is to minimize the losses when they leak.
That’s the point: you can’t just pile every website into the same zone, and if you did pile them into the same zone, then using a different password for x.com and y.com is to some extent pointless because x can observe y’s password input and vice-versa.
(disregarding the fact that in current computing architectures “just put all the untrusted stuff on one core” is probably an insufficient solution due to shared caches anyways, no indeed nothing in this attack requires “sharing a core”)