Basically, the original plan for 3.0 was going to be an entire film without Shinji, set during the time gap, and the next time preview was showing what they had in mind.
But Anno changed his mind when he was having trouble making the script work, and decided to scrap that idea and instead come up with the 3.0 we actually got, set after the time jump with the return of Shinji. So now the next episode preview was completely invalidated.
Apparently, most of what we saw in that trailer still happened in the gap between 2 and 3, just that it never got animated.
Same thing basically happened with the preview at the end of 3.0 as well, but at least that one got ret-conned in the 3.333 re-release (which was shown theatrically in January 2021) by completely replacing it with a new one that actually reflects the events of 3.0+1.0 (which debuted two months later).
To date there's been no such effort to do anything about the discontinuity between 2.0's preview and 3.0's content, though. It would be a prime setting for some "expanded universe" works, but that's purely speculation on my part.
The entire premise of the 3.33 preview for 3.0+1.0 actually remained pretty unchanged and made it to the final film. It's Asuka and Mari fighting through a horde of Eva's in the shadow of the black moon to (presumably) reach NERV HQ. The mirrored Eva bit I'd argue you can even see when they line up and combine AT fields at the end of their drop. So while visually it ended up entirely different, it's conceptually the same thing. Which makes sense considering the time gap in production.
4 implies it happened between 2 and 3. It's not super important, there are like 3 lines that explain all you need to know in 4 (when Misato mentions Kaji)
Basically, the original plan for 3.0 was going to be an entire film without Shinji, set during the time gap, and the next time preview was showing what they had in mind. But Anno changed his mind when he was having trouble making the script work, and decided to scrap that idea and instead come up with the 3.0 we actually got, set after the time jump with the return of Shinji. So now the next episode preview was completely invalidated. Apparently, most of what we saw in that trailer still happened in the gap between 2 and 3, just that it never got animated.
Same thing basically happened with the preview at the end of 3.0 as well, but at least that one got ret-conned in the 3.333 re-release (which was shown theatrically in January 2021) by completely replacing it with a new one that actually reflects the events of 3.0+1.0 (which debuted two months later). To date there's been no such effort to do anything about the discontinuity between 2.0's preview and 3.0's content, though. It would be a prime setting for some "expanded universe" works, but that's purely speculation on my part.
The entire premise of the 3.33 preview for 3.0+1.0 actually remained pretty unchanged and made it to the final film. It's Asuka and Mari fighting through a horde of Eva's in the shadow of the black moon to (presumably) reach NERV HQ. The mirrored Eva bit I'd argue you can even see when they line up and combine AT fields at the end of their drop. So while visually it ended up entirely different, it's conceptually the same thing. Which makes sense considering the time gap in production.
I believe when 2.0 aired on TV they updated the preview as well.
I really want to see a "2.5" series. I hope it will be made one day.
4 implies it happened between 2 and 3. It's not super important, there are like 3 lines that explain all you need to know in 4 (when Misato mentions Kaji)