5e does not have a similar Corruption rule for the Nine Hells

Some of the planes have optional rules, as presented in the DMG.

The Nine Hells does have an optional rule, but it's not corruption, it's called "Pervasive Evil" and doesn't do the same thing as what you were looking for (DMG, p. 64):

Pervasive Evil

Evil pervades the Nine Hells, and visitors to this plane feel its influence. At the end of each long rest taken on this plane, a visitor that isn't evil must make a DC 10 Wisdom saving throw. On a failed save, the creature's alignment changes to lawful evil. The change becomes permanent if the creature doesn't leave the plane within 1d4 days. Otherwise, the creature's alignment reverts to normal after one day spent on a plane other than the Nine Hells. Casting the dispel evil and good spell on the creature also restores its original alignment.

The Abyss has an optional rule called "Abyssal Corruption", which is on page 62 of the DMG, but
a) it isn't to do with the Nine Hells, and
b) it still isn't anything like the optional rule you were hoping to find.

If you are the DM, you could always come up with your own optional rules for any plane, but as it stands, RAW, the Nine Hells only has "Pervasive Evil".

Warlocks with fiend pacts are mortals,¹ and therefore do not have any relevance to any fiendish hierarchy—in life, anyway.

Fiend-pact warlocks are rather likely to find themselves on the Lower Planes after death, either because they actively enabled an evil entity to advance its aims on the material plane and thus are judged evil themselves, or because they explicitly sold their souls to their patron. In the latter case, that soul is now a commodity, not an entity. What their fiendish patron does with it can vary; it can power various foul magics, serve as food or entertainment, or it can be put to work. Mortal souls become fiends naturally on the Lower Planes, so at some point—if not consumed or destroyed—it will become a fiend itself, and then it will have a place in the appropriate fiendish hierarchy.

Orcus, demon prince of undeath, famously followed this route. Whether he was a “warlock” per se is irrelevant,² point is that his soul found itself in the Abyss, and eventually became a dretch, and accrued power from there.

Tieflings do not really have any formal place in the hierarchy; if they are useful pawns, then they will be used as pawns, but aside from that they’re regarded as weak and replaceable. It’s hard to prove a negative, but I have not seen them included in the various fiendish hierarchies, nor described as being eligible for promotion to other fiendish types, even the lowest-rank options like dretch or nupperibo/lemure.³

1. _{I mean, unless they’re not. Fiends and other outsiders could conceivably become warlocks, too, and a fiend making a pact with a more powerful fiend is not at all unusual. But the pact doesn’t necessarily change their place in the hierarchy. It presumably makes them stronger, which obviously matters, but how much is going to depend on the exact pact and what their patron is offering, and how much that affects their placement is going to depend on how that’s viewed by their peers.}

2. _{The warlock class didn’t actually exist when Orcus was first published in 1976; he was just known to have been a spellcaster in life. At the time, the only arcane-spellcasting class was the generic “magic user,” since Orcus debuted in the fourth-ever Dungeons & Dragons book, Eldritch Wizardry. The warlock as we know it today didn’t exist until 2004’s Complete Arcane supplement for the “3.5e revised edition” of Dungeons & Dragons.}

3. _{Nupperiboes are actually—and this is an incredibly closely-guarded secret—the lowest form of ancient Baatorian, rather than the modern rulers of Hell, the Baatezu. They are shredded and rendered into lemures, the lowest-rank Baatezu; most devils—most everyone at all—believes this is done simply because nupperiboes cannot be promoted to other types of devils, while lemures can. But that’s not quite right—they probably can be promoted, but that would be to other forms of Baatorian devil instead of Baatezu devil. Part of the Baatezu’s “might makes right” hold on Baator depends upon this practice to prove their dominance over what’s left of the Baatorians, who might otherwise be seen as the “rightful” rulers of Hell. This matters a great deal because Baator is a lawful evil plane—the Baatezu’s claim is only valid to Baator if the Baatezu actually control the plane, and that means eliminating any potential rival claims. So the high-ups in the Baatezu hierarchy—particularly Asmodeus—make a point of ensuring that the nupperibo-to-lemure process is extremely thorough. Most of Asmodeus’s power comes from Baator itself, so he cannot allow that to slip. Baator does the Baatorians no favors, though—most everyone believes nupperiboes cannot be promoted because they never seem to, and a lot of that has to do with the Baatezu dominance of the plane suppressing that.}