There are plenty of ways to do 'too angry to die' that don't involve siphoning HP from your enemies. There's a reason why players pretty much universally refer to it as life steal.
The term 'Second Wind' is an athletic term. You're fatigued, out of breath, and unable to continue. And then you suddenly find the strength to press on. It's similar in concept to 'Thrill of Battle' really, in that you're relying on a burst of adrenaline to keep you going. That's why you punch the air after using it. If they wanted to be mean about it, these sorts of effects would be temporary HP, causing you to collapse from fatigue after. But I can see where they're going with it at least. I don't recall Souleater being directly referenced in the DRK quests. In older games, Souleater did damage you. In this game, it's someone else's soul being 'eaten', through both the animation and sound effects. They could have gone either route with it, but their current implementation makes sense.
I have no problem with non-spell self-healing. As I've suggested earlier, there's nothing wrong with a Berserker type having superhuman regeneration or adrenaline/second wind type effects. There's nothing wrong with having iron skin, temporary HP, or stat bonuses. These things are actually quite common, and that interweaving of offense and defense is something that used to be intrinsic to WAR back in Heavensward. I just don't see how they're able to absorb someone's HP by hitting them. I'm open to suggestions, but it's something that needs to be explained visually through the job action design.
As I've said earlier, I actually don't care what DRK's theme is. I just care that there is one, and that it feels unique. When TBN was released, it felt really unique, and the aesthetic of DRK's bubbles matched up really well. I would have just doubled down at that point and focused on it. If you have a problem with DRK absorbing damage through magical barriers, that's fine too. Just come up with a new mechanic that's unique to DRK, but please just be consistent about it. I don't want to see the same thing copied over on to WAR or PLD just because players begged for it.
And WAR isn't about high HP, any more, really. Thrill is the only action that adopts that approach. If I were designing the kind of tank that you're describing, I'd build WAR's entire kit around them building up massive pools of temporary HP. I remember up until Stormblood, players were coming up with creative ways to see how high they could push the HP pool. That was incredibly fun. I don't think that the excuse 'b-b-but this is the way things are' really cuts it. If you have even the slightest bit of an imagination, I'm sure that you can come up with something more identity defining than what we currently have.