Also frequently when using things like peeling noise is to use different scale and resolution of the noise itself. While on smallest scale there might be 1 noise value per minecraft block. You can can also use a different scale in that 1 noise value is used per 10x10 minecraft chunk (16x16 blocks?)

Also not sure how familiar you are with noise generation like perrin but things have slopes to them and isn't just completely random per point. So even without seeing generated data. You can infer a little bit about the next value depending on the intensity and resolution.

Lastly, you can just not use noise at all and just place things at given coordinates and make the game incorporate them into the proc gen at chunk time. E.g. you want a city always at 1000,1000 coordinate far away from 0 0. When you get near you can apply smoothing filters in and around the 1000 1000 position thru various math and layering systems so no matter the proc gen at that point. City can be there and it not look completely out of place.

Sure you do. When you want to apply tectonics to a chunk, it's easy to calculate (and cache) the pre-tectonics version of all the neighbors.

The problem isn't effects that need to know about their neighborhood, it's effects that need detailed info from 50 chunks away.