Iuz is not called out that way, though. And one instance of a demigod becoming a lesser god doesn't mean that they all did.
Except it's not just one god being called out.
In 2e and 3e, Gwaeron Windstrom, Valkur, Jergal, Hoar, Laogazed, Kiaransalee, the Red Knight, Urogalan, Haela Brightaxe, Deep Duerra, Shevarash, and Selvatarm were
all demigods--and they
all grant spells in 5e, which means that they are all at least lesser deities by 5e standards.
With Lurue being referenced in the DMG, and Iuz in the PH, that's
fourteen examples of former demigods now being treated as full-fledged gods who are able to grant spells. The only thing unique about Iuz is that there haven't been any other
Greyhawk demigods referenced--but as I said, there's over a hundred GH gods and only twenty are referenced at all. And frankly, most of the Greyhawk demigods are kinda dumb.
And all of the Lesser Idols in Exandria are given cleric domains in addition to appropriate warlock pacts.
And coupled with the DMG stating that demigod is basically a
species (half-god, half-mortal),
not a divine rank or level of power or what inevitably happens if a mortal undergoes apotheosis, I think that fourteen examples are enough to make it a fact: Iuz is a god in 5e, not a demigod.