I find this hilarious: When the 4e players desired to find similarities between 4e and previous editions, they went out of their way making all sorts of rational explanations with examples but with 5e they find all sorts of excuses and reasons not to identify similarities.
There are a lot of 4e fans and former-4e-now-5e-fans. We don't all get together to compile approved talking points so that we never contradict eachother.
Then there's matters of extremes. If someone says "nothing from 4e can ever work in 5e" that's a pretty extreme position, and the tattered fragments of 4e that exist in 5e stand (or flop about weakly) as clear counter-examples to it. The other extreme, "everything you could want from 4e is already in 5e" is equally absurd, and the same examples conclusively contradict it.
The save per round against conditions was used in 4e. It is used again in 5e and due to a different chassis the DC is higher. Attempts to obfuscate this similarity doesn't change that fact.
Save every round with a bonus based on stat/class/level vs specific spells was introduced in 3.5 and and is used by many more spells in 5e. Save every round at ~50/50 regardless of stat/class/level for death saves and for virtually any condition with a duration other than 1 turn or all combat long, was a 4e-ism. 5e uses it for death saves, only. Really, 3.5 introduced a mechanic, 4e took it much further, and 5e dialed it back most of the way. There's a lot of that in 5e, often, it even dials stuff back from 3.5, like feats and multi-classing, both explicitly op-in for the Standard Game.
One needs to keep in mind that in 4e conditions were quite common and easy to put into affect (hence the standard DC). It is easy to 'forget' that fact when one is biased in not admitting the similarities between the two systems.
That just highlights a difference in attempting to establish a similarity. Self-defeating, that.
Yet there's a much clearer similarity in Death Saves.
A different system like 5e required an evolution of the Surge Mechanic, hence the HD, but that doesn't mean HD did not derive from the Healing Surge. Therefore it is a 4e inclusion.
Sure, it's a partial inclusion of the idea of surges. Their nature is similar, but their function in the game is very different. Depending on what you (dis)liked about Surges, you can find HD to be an insultingly bowdlerized parody of Surges, or an intolerable contamination of 'real D&D.' And, HD are also still what they were back in the day: what you rolled to determine your character's hps. So they're not an evolution of Surges, more a hybridization of surges with old-school HD.
Yet, as dissimilar as HD and Surges are, HD do let you quickly (1 hr is quick in this context) recover hps without magic.
A much stronger example: overnight healing and heal-up-from-0 was taken straight from 4e to 5e. Heal-from-0 in 5e can easily be seen as a rare actual 'evolution' from 4e, in that 4e, like 3.5 & AD&D tracked negative hps, while 5e has dropped that vestige of the earlier systems in favor of being purely heal-from-0. Another example (the only other example I can think of atm) would be Advantage, which is a clear evolution from 4e Combat Advantage and various roll-twice & re-roll mechanics. Combat Advantage consolidated more complex modifiers and loss-of-DEX-bonus conditions into a single one, and Advantage further consolidated CA and other bonuses with roll-twice/re-roll mechanics, /and/ consolidated penalties & roll-twice/re-roll mechanics into Disadvantage.