A lot of answers on here oppose the idea of “brand identity” and want to emphasize instead the site’s purpose, how accessible it is, how well it functions, and so on. But I would like to make a few comments in terms of the brand.
It’s hard to put into words, but both of these designs evoke someone trying to be StackExchange. It feels like one of the clones, or like a site for a company that doesn’t exist yet beyond VC funding and a website: that wants to pass itself off as older and more authoritative than it is.
And I do really like some things about these designs. I see the appeal of Cyberbougie and Nu-Brutalism. The colors evoke Michael DeForge and programming color schemes; the text reminds me of Compact Mag; the style suggests a similar intended user base to Canva. They’re absolutely on-trend—but that’s the problem here!
Something feels wrong about making it follow trends of web design: following is for followers. It suggests that StackExchange is imitating or trying to be something else. But it isn’t.
StackExchange already has an incredibly powerful brand.
StackExchange in the same category as Wikipedia: it’s infrastructure. As you say in the blog post, it’s a spine and backbone for the rest of the internet.1
StackExchange is the real thing.
By analogy, consider soda pop.
Poppi is Paperback Chic, which is appropriate for its brand identity. Poppi is fashionable, it’s of the present day, and its product is a nod to soda. Its brand is about the brand of soda: it says, “what if we took soda, but put a new twist on it?”

Now imagine if Coca-Cola wanted to go Paperback Chic:

Awful, right? The power of Coca-Cola’s brand comes from the fact that it is foundational to the idea of soda. You understand Poppi in terms of soda, and you understand soda in terms of Coca-Cola. They can afford to have a logo from the 19th century painted in loopy cursive.

Coca-Cola’s power is in its legacy, not in its youth. A soda brand looks like Coca-Cola or doesn’t, but Coca-Cola shouldn’t try to look like a soda brand.
Well, StackExchange shouldn’t try to look like programming, because programming already looks like StackExchange.
The more “design” there appears to be, the less “real“ it looks.
Of course everything has a design; the point is that some designs announce themselves more than others. Consider Wikipedia’s (in my opinion excellent) redesign. They added features, they tweaked the look a little bit, but mostly they just reorganized the layout of the page to make it easier to navigate. It’s still very much a classic website: a nice, clean, sturdy thing with useful information all over it.
Wikipedia feels like it will always be there. Wikipedia feels like it will still work at the bottom of the ocean. Wikipedia feels real. They should keep it that way, and so should we.
Because this site is actually pretty great as-is.
1 By the way, I’m a little bothered by the stack connected into a spine.

The once disparate stacks now connect to form a spine or backbone — representing our ambition to reprise our role as a vital source of knowledge for technologists.
I get the metaphor, but recall that “stack” is already a metaphor: a stack is a data structure that stores and retrieves individual units of information, like a Pez dispenser holding a stack of candy. You push things onto it and pop things off one at a time. But now we can’t? The candy is fused together into a cluster of homogeneous content?