Basically 4E. Rapid overnight healing, +2nd wind+ HD based healing.
It's interesting how perspectives differ on this. From what you're saying, 100% healing, Second Wind for a single, specific class (as opposed to a generic ability), and HD (which are carefully used so they don't interact with any class/monster abilities and thus can be easily removed) mean "4E won!".
Whereas for me, from a 4E perspective, that seems like a pretty strong move away from 4E's model. Specifically:
1) Healing overnight was rarely a big issue in 4E, in practice, it was there largely to simplify book-keeping, rather than to "fix you up" (regaining all your Healing Surges was a far more important part of it, generally speaking - you don't even regain all your HD by default in 5E, I note).
2) Second Wind was a big 4E thing, I agree - but only because it was available to all classes, and metered by Healing Surges. The thing they've called Second Wind in 5E is a cool power, but it isn't in any way 4E's Second Wind, because it is class-specific and totally un-metered.
3) HD are only superficially similar to Healing Surges. They are actually close to the opposite, design-wise.
Healing Surges are the absolute core of 4E's healing system.
Everything about it revolves around them. They allow you to potentially heal between 200% and 400% of your HP, per day, in practice (depending on a bunch of factors), sometimes even higher (with healing-oriented Clerics around, for example). But it is they who determine if you can be healed. If you're out of Healing Surges, you're in trouble.
HD completely excluded from 5E's core healing system, by design intent.
Nothing revolves around them. They are simply a form of "bonus healing" that
replaces stuff like bandaging in earlier editions, are actually more limited in many ways (especially at lower levels). Assuming default HP and no CON bonus, you can likely regain 60-90% of your HP with HD - vastly lower than you could via Healing Surges (even a class with only six healing surges, which I think was about as low as it went, and only using Second Wind and resting, could regain 150% of their HP in 4E D&D - any help at at all, or more surges, and it was vastly higher).
Please note that, as per the Basic set, 5E has no bandaging or equivalent, and Healers Kits can only be used to Stabilize people (they have no other formal purpose), and Medicine skill only to Stabilize people or diagnose illnesses. I presume DMs would allow more uses for it, and players find them, but there's no rules for bandaging or anything similar, that I can find.
So for me, it definitely isn't "basically 4E". It's not a "numbers" or "semantics" thing, either - it's a fundamentally different design, and one which doesn't actually closely resemble ANY previous edition of D&D. It
looks a bit like 4E, in the same way that, at a glance, but it's a superficial resemblance at best.
Having followed the discussions of what they were going to do with healing in 5E pretty closely during development, to me it looks like they didn't "pick a side" at all, but rather they made a compromise decision. The sides, from what they were saying, appeared to be "like 4E" and "like 3E", by and large, and what we've got isn't really like either.
YMMV, etc.!