This to me seems more a WotC-era thing, though it's been around since 1974.
Yeah, prior, it felt as much like coincidence as design - plus the balance-of-imbalances of the TSR era wasn't just over an adventuring day, it was over the whole campaign.
what about a situation that would normally be three encounters (let's say at a castle: gate guards, pet wolves in the kennel, ogre blacksmith in the smithy) that gets turned into one long rolling battle
In any version of D&D that has anything like encounter design guidelines, if it /was/ three encounters, well, the party will be in bad shape and have completed three encounters. If it was three trivial non-encounters that finally add up to the equivalent challenge of one, it'll be one. Not particularly perplexing. I'm sure there may be middlegrounds, depending, where 3 easy encounters add up to one deadly or something, in which case, well, still kinda up to the DM, like basically everything else, huh?
In terms of a hypothetical encounter-based game (which D&D has never been), though, I'd say it's one encounter.
The neutral answer, then, becomes in-game time.
Nothing 'neutral' about it. Arbitrary, perhaps is the word you're looking for.
5e went this route with 1-hour rests and IMO overdid it; but the idea of powers refreshing daily is far more believable in the fiction than having them refresh after x-number of battles and-or encounters.
Nothing about n/rest resources is terribly believable. We're used to 'em, after decades in D&D, but they're really kinda nonsense.
Can't speak to HD but for h.p. any character - while not knowing the exact numeric value, of course
There you go. The players are dealing with meta-game numbers, the character is imagined as dealing with in-fiction pain (& disability, that is /never/ modeled in the rules). "Realistically," a human being can be on the verge of death and not even suspect it, or certain his time's run out and be fine.
In the fiction, though, the wizard knows from years of training that it takes sleep to recharge his magical powers; and the cleric knows it takes a prayer session each morning.
In 3e, the latter could be literally the case, the cleric just
dinged at his appointed hour.
Complete aside, though, the
15MWD first came up in games I was actually in way back in the day, because of that need to
sleep ('cause that's what the rules said) after casting
one spell, as little as 15 minutes after waking up. (Wake up, memorize your spell, cast it...
zonk! 15MWD.) It always seemed goofy. Anyway, in some REH pastiche, don't recall which one, sorcerers used "Black Lotus" to enter supernatural dreams that re-charged their powers.
That might be an interesting (ie dangerous) option for casters wanting to recharge more frequently, especially in a gritty pacing game, or under FrogReaver's variant.