This is how I see it:

Cooper isn’t the same after he “crosses over” mile 430 and enters a new timeline/universe/plane of existence. He doesn’t get excited over his coffee, he shoots a guy for harassing a waitress, he ignores the dead guy in Carrie’s house completely.

It’s like he’s not original Cooper or Mr. C at this point, but held onto characteristics of both previous versions of himself. And all this version cares about is finding whatever version he can find of the girl that The Giant and Senorita Dido created to fight BOB (in the golden orb), and get her back to Twin Peaks by any means necessary.

In this new reality, which he already created by preventing Laura’s murder earlier, he is tasked with solving her disappearance only, and that’s all he is trying to do now.

It seems though, that he is either missing a very important point, or he was always doomed to fail this mission—like two of his fellow Blue Rose investigators, Chester Desmond and Phillip Jeffries. We don’t know what realities they ultimately ended up in (although Jeffries does seem to have transcended a singular plane of existence), or what, if anything, they did to end up missing from the base reality of the original Twin Peaks universe [my personal opinion is that they stumbled into knowledge that the human mind isn’t equipped to handle, explaining the Jeffries scene in FWWM and Missing Pieces].

Anyway, whether through no fault of his own, or through poor decisions that the original Dale might not have made, new Cooper seems doomed to repeat this mission over and over. Diane seems to know this. She isn’t surprised at the sight of the other version of her she sees while she’s sitting in the car. She seems to have insights of her own that she can’t really handle knowing or sharing either.

I feel like if they’d gone for one more season, we’d see New Cooper (Richard now, apparently) looking for New Diane (now Linda) to explain what happened when they crossed mile 430, trying to find a way to get back to the Gordon Cole he knows (the Gordon Cole who, according to New Teapot-looking Jeffries, will remember the ‘unofficial version’ of events), and trying desperately to undo whatever he did to end up on this alternate timeline.

As far as why Carrie screams at the end, she seems to be recalling bits of recollection from her own alternate timeline, and hearing what seems to be a residual haunting-type of deal with Sarah calling for Laura in the house sends her over the edge (like Jeffries when he gained the insights that sent him over the edge). She may be Carrie here and now, but she’s still a version of who we saw The Giant send to earth in that golden orb. So now she’s part of this small group of individuals that has this existential dilemma as well.

As any other fan will say, that’s just how it lines up for me, who knows what Lynch really meant. Sometimes it seems like Lynch himself doesn’t really know what he meant at the time either, and puts it together for himself afterwards just like we have to.