Alexis Rose from Scitts Creek does it all the time, like when she gets frustrated with Johnny she'll be like "Dad-uhhhhh"?

It seems stereotypically like a "white girl" thing, often affluent

Vocal fry

It's an offshoot of the whole valley girl thing from the seventies and eighties, iirc

At least, that's the general origin of that specific expression of the over exaggerated brat whine.

Other versions likely have other origins, and the long extended vowel at the end is likely timeless

Vocal fry is different.
I have kids that went through Tue stages.

Vocal Fry is the down long stretch with the frying of the voice sound, usually showing general disinterest. Like Gawwwddd.

The kind where they say Gawd-duh is two syllables and shows genuine exasperation as its said in a had higher tone and distinct emphasis on the extra syllables.