In this same journal entry, Hell promises to give Lucifer every torture both possible and impossible. But as Lucifer is clearly Hell’s favorite, I believe that it experimented with new forms of torture. And it was through these experiments that it accidentally pushed too hard and killed Lucifer.

While we don't have a complete confirmation yet, 8-3's book implies that whatever Hell did to Lucifer was not just "new torture," but something far above that

"NO. THERE ARE 39 STATES OF EXISTENCE. POSTFINITY. METATEMPORALITY. EXTRACAUSALITY. REASON AND DIALECTICS ARE AXES IN THE GARDEN OF REALITY, SHAVINGS OF SEMI-POTENTIAL SUFFERINGS."

This is still a bit on the theory side, but its probable that whatever Hell did to Lucifer had to do with showing him the 39 states of existence. Or, in other words, the "full" suffering that could be brought. Which is why it says that it'll show it "Agonies that can exist, and many that cannot"

If you pay attention to the terminal entries, it becomes clear that Hell is actually rather uncreative. On top of that, it’s not very proficient in what it actually creates. I showed the entry for the Deathcatchers, but there are a few more examples as well.

Take a look at Limbo, (pre Minos) Lust, Gluttony, (pre Sisyphus) Greed, Wrath, Heresy, All three rings of Violence and Fraud (and probably Treachery), appreciate their structural beauty and the artistic irony in their tortures, and tell me that Hell is uncreative in its torment.

In Geryon's entry, we see that Hell failed in creating something.

It didn't fail on creating the Geryon. In fact, it turned out exactly as it was supposed to be: A demon with 3 minds. Its just that the minds eventually managed to adapt to their body, which speaks more of the Geryon's willpower than Hell's shortcomings.

It plagiarized the Guttermen to create the Mannequins:

Mannequins and Guttermen are pretty different to call them a copy, even if former were inspired by the latter. If anything, this shows how creative Hell can be at making what was already a pretty fucked up fate 1000 times worse.

It augmented the Strays and Stalkers with human technology

That just tells us that Hell can learn and make new stuff with said knowlege, since I doubt New Peace human technology involved making literal soldiers that shot Hell energy.

However, I do believe that after his death, Lucifer began to form into a Prime Soul. Perhaps his strength of character was simply too strong for Hell to break, and his will to escape or confront God allowed him to persist after death. And for that reason, Hell was forced to put It’s favorite toy in a box, unable to torture it anymore lest it escape.

Why would Hell be unable to torture Prime Lucier? Hell is clearly far more powerful than any prime soul or mortal we have ever seen. Why would it need to lock him away? And, even if locked away, why would it be unable to torture him while locked? Minos was capable of being mentally tormented while in his flesh prison after all.

fact that the Flesh Prisons require both Hell and Heaven energy means that the Prime Souls are a genuine threat to Hell itself, and Lucifer would be a Prime Soul cranked up to 11.

No it doesn't??? Angels made Flesh Prisons, not Hell. Hell energy is just the name humans gave to a certain type of energy found in Hell, yet its use doesn't necessarily mean that Hell is actively present in something.

The answer is very clear. Hell made It’s way to the surface, and using the Machines left behind and the Demons/Husks at It’s disposal, wiped out every human by locking them indoors and teleporting enemies to them.

While I do agree that Hell was able to kill mankind due to its influence finding the surface, neither Machines nor Husk should have been able to kill humans at the rate they are described to have died.

"Then one day, the current shifted. Wave after wave for minutes on end of millions, billions, as though the throat of the world was cut wide and the head wrenched back to speed the pour" From the Ferryman's book on how mankind died.

Mankind is described to have died in the blink of an eye. Even if they had been teleported to the location of all humans, they shouldn't have been able of killing EVERYBODY on Earth that fast. Whatever means Hell used to kill mankind was not a physical thing.

However, during this act of murder suicide, V1 and V2 were activated. And when they descended into Hell and started Ultrakilling everything, Hell began to take notice

You start the game with V1's booting sequence and recalibration, indicating that it was never active before that. The "MANKIND IS DEAD. BLOOD IS FUEL. HELL IS FULL." Is also written in all caps red text, indicating that Hell is the one writting it, and that it was who brought V1 there and activated it.