Huge chunk of text uwu

I feel like it's good that you pushed the attack speed to be based on the amount of his Blood Well, rather than just occur when his Blood Well is full. However, Unleashed is on WAY too short of a CD. Every 30 seconds, you have GA, and since it also just REFRESHES when you exit combat, you basically always have it up. Not to mention, I'm not too sure why you have two resources filling up your bar instead of one; from a quick glance over your kit, I don't see Suffering being used anywhere else, and in my experience, two different resources just tends to make your kit unecessarily complicated. I'm also not a fan of the HP costs on Aatrox, since it just means you take more damage, even though you're a sustained fighter who wants to stay healthy.
Q heal is interesting, and I like it a lot, but it still holds the issues that the current one does; it's super strong, but it's incredibly telegraphed, super easy to dodge, and leaves you vulnerable for the entire time you're doing it due to how long it takes to activate-- hence why, as an Aatrox player, I didn't end up using it too much during a fight as I did to engage a fight. Not to mention, if you're knocking them out of the area now, instead of up, it pushes them away from you and makes it harder for you to get on top of them. I'd say work on changing it more from his current one.
I like that on kill your W gives you benefits-- I like that a lot, actually. After all, Aatrox thrives on battle,  so it makes sense. Again, though, not a fan of health costs. The auto reset also seems kind of tacked on, though.
E is good, too, since it helps Aatrox's inability to stick on targets-- he's super susceptible to being kited. At the same time, it can lead to interesting moments where you lower a minion wave, skewer them all with E, and then run at the enemy angrily. I'm always a fan of running at people angrily :^)
R is... odd. It fills your meter by a percentage equal to half the damage it did, but it's AP scaling. I'm, uh... also not sure why you'd ever use your ultimate, considering it kills you. So, it puts you in a position where you proc it-- and then get popped. Your passive activates, and then it kills you instantly. While I see where you were going, for it to interact with and combo with your passive, I feel like it wouldn't work.
You also have the issue of "wait what do I build?" As of right now, Aatrox has *five* builds; attack speed on-hit, attack speed bruiser, full tank, critical strike, and lifesteal. This has the similar issue of having a lot of different builds that people aren't sure what to build specifically; I've seen high ELO players trying Aatrox and saying "go crit, it's the only way," as well as others saying "go full tank, it's the only way," and while I've only ever had success with an attack speed on-hit build, I've seen Dong Huap have good success with a more bruiser-based version, and I've seen somebody say they were able to make Lethality work because of loading damage onto the Q and W damage-proc.