The DMG section on running combat (p.247-248) has this to say:
Most DMs track damage in secret so that their players don't know how many hit points a monster has remaining. Whether you choose to be secretive or not is up to you.
Players often ask how hurt a monster looks. Don't ever feel as though you need to reveal exact hit points, but if a monster is below half its hit point maximum, it's fair to say that it has visible wounds and appears beaten down. You can describe a monster taken to half its hit points as bloodied, giving the players a sense of progress in a fight against a tough opponent, and helping them judge when to use their most powerful spells and abilities.
And since the Fighter's Battlemaster has a class feature (Know Your Enemy) that can tell you their HP in a very vague way, whether they have more or less than you do, it seems clear that the game at least expects HP to be secret information, while allowing that some DMs may decide not to hide it.
Most DMs, including me, give some kind of general indication of how much HP a monster has left using general terms like the "bloodied" reference above, which originates from 4th edition using that term to mean "below half health" (a good idea used -- perhaps overused -- in 4e to trigger a dramatic difficulty or style change in the fight). Many DMs describe being above half health as "unhurt" or "barely injured", below 50% as "hurt" or "has taken a few hits", and then at very low HP, perhaps 10%, phrases like "in really bad shape" or "barely standing" are common. There's usually nothing more clear than those, though, and definitely nothing numeric.
At my table, terms like "barely standing" are usually code to let the players know that the creature has only a handful of HP left; they can expect to take out the monster with a single hit of a basic weapon attack or cantrip. I'm letting them know they don't need to expend any resources on finishing off that target. Once in a while when an attack just barely fails to drop a monster I'll say something like "Ohhh! He's got two hit points left!" or "He survives that hit with one HP!" just to ramp up the tension. (But depending on the hit, I'm just as likely to ignore the last couple HP -- it's dramatic and fun to have a monster get finished off with a huge crit or incinerated by a fireball, so I have no problem with fudging in favor of the players there.)
I personally have never seen a problem with the metagame implications of Power Word: Kill, sleep, and similar spells and effects that depend on specific HP totals. Yes, there's a tactical decision to make there. Do you throw the spell now, or hold back and deal some more damage first? If you throw it too early, you waste the spell on a creature too strong for it. If you wait too long, you waste some of the spell's potential output, possibly taking more damage than you had to.
But that is, as they say, a feature, not a bug. Using those kind of spells is something of a gamble, and that's one of the balancing factors to them. I don't think you should be able to use spells like that with absolute certainty that they'll work. There's no save, so you have more control than you would otherwise, but it's never a sure thing.