Advanced Fluid Handling 2 is available almost immediately after you unlock blue pipes. Advanced Fluid Handling 3, though, requires going far past you unlock black pipes, needing Chemical Engineering 3. Because I make heavy use of these pipes I wasn't really able to do much with the fancy new black pipes I unlocked, making the tech itself kind of a letdown. It would be convenient if you could research it AFH3 right after you get black pipes, since none of the items require any ingredients past black pipes and chemical-era stuff. For convenience, it's line 848 in override_mod.lua:

data.raw.technology["advanced-underground-piping-t3"].prerequisites = {"nullius-chemical-engineering-3"}

Advanced Fluid Handling 3 is only about a third of the way into the physics tree, so it's really not all that far beyond pipe 4 in the grand scheme of things. One reason that it is where it is is that Advanced Fluid Handling 2 is about halfway through the previous tech level. If they're too close, then it's really stepping on the toes of the previous tier, and too easy to just skip the middle tier entirely. It would be nice to move pipe 4 a little later for the same reason, but that's complicated since it's an ingredient in so many of the final tier buildings that unlock in early physics. Advanced Fluid Handling isn't an ingredient, so that tips the scales toward delaying it a bit longer.