I had a great literature teacher who took pains to point out all the wordplay in Shakespeare's plays in the context of the culture his time. I recall a surprising amount of them being pretty naughty double-entendres! Some of our slang today can still be traced back to those.
However, their meanings were still static in nature, even if manyfold and cleverly embedded in there. E.g. when he coined new words, they had a meaning you could derive from the context. Unlike "Skibidi," which is essentially meaningless and can be stuffed anywhere randomly!
To put it another way, I would not put the kids I overhear these days anywhere near the skill-level of the Bard ;-) Brain rot is very dynamic and off-the-cuff, with a key enabler being that meaning can be entirely optional. And they riff off of each other and random memes. Almost like jazz in some sense.
I think what you said at the end makes sense. There's always been a language barrier between generations, but the gaps are growing faster. As the world gets weirder and weirder accelerated by technology, human language is evolving in ways that are surprising.
It used to annoy me that many SciFi authors would immerse you in the jargon of some unrecognizable, futuristic culture without any exposition, forcing you to figure out over time -- and sometimes guess at -- what words meant. Now I'm living it!