"Why everything is ‘aesthetic’ to Gen Z and Alpha/'Aesthetic' is now an adjective and a one-word compliment. Why does it still sound wrong to older ears?"

That headline at the Washington Post sent me right to the OED to see when "aesthetic" first became an adjective. 

The relevant meaning is "Of a thing: in accordance with principles of artistic beauty or taste; giving or designed to give pleasure through beauty; of pleasing appearance." The OED traces that back to the 1800s:

1855 — We had just completed a not very æsthetic quantity of boned turkey.
Musical World 21 April 181/1

1862 — I heard an exquisite ask a lady ‘if she snored?’ She..said, ‘No, I do not.’ ‘I am glad to hear it—it is not a very æsthetic process.’ Life amongst Colliers iv. 83

1881 — The little coffee-room, too, had been papered fresh with a modern æsthetic wall-paper—the steady march of culture and taste is so fast and unflinching everywhere!
G. D. Leslie, Our River ii. 31

Another adjectival meaning is to refer to a person who has good taste, but that's also from the 1800s: "He is highly aesthetic, but not very genial" (1844), "My first impression of him at college was of a purely æsthetic man" (1860).

So what is the WaPo article going on about? Apparently, younger people have been annoying older folks by using "aesthetic," the adjective, a lot, and some older people, instead of merely complaining that the word is overused, are snottily asserting that "aesthetic," the adjective, is not a word. If you're going to act like this, you'd better be right:

@gqtrendtalks Maya rudolph with Jimmy kimmel #mayarudolph #jimmykimmel #hollywood #viral #fyp ♬ original sound - GQ trend Talks

"They use the word ‘aesthetic’ in an improper way. They have now taken words and made them new words, which is not a thing"... but first, it is a word and has been for a long time, and second, you absolutely can make new words, and it totally is "a thing." 

Nouns are repurposed as adjectives all the time. We easily say "coffee cup" and "car key" and all the many variations of that kind. But we don't so easily say "That cup is so coffee" and "That key is so car." And these kids today are saying things like "That's so aesthetic."

If you want to delve into what's going on there, grammarians speak of "attributive nouns."