A common way to get around explicitly giving the HP of a monster and telling them nothing is the "They look... " rule. When they ask how many HP the baddie has left, tell them "They look injured, but not enough to hinder them" or "they look bloody and totally messed up" etc. As a rule of thumb, you can decide their health into quarters and come up with a common phrase for each, or come up with them on the fly depending on the situation: "Grog's hammer has left some of its ribs broken, but it looks healthy enough to keep fighting for a while."

4e had a specific status called "bloodied" that creatures gained when they dropped below half HP, this represented that one of the attacks on them has been a telling enough blow that they're showing signs of injury. I brought this with me to 5e, because it's a useful contextualizer for players to get a feel for how well they're doing.

One advantage of this system (especially for new DMs) is that if you massively overspec an encounter and the players are in trouble, you have some time to realize it's going badly, and can drop the monster's HP pool a little to compensate.

One advantage of this system (especially for experienced groups) is that if the party are doing badly, and haven't realized it - the moment you say "right, the enemy is bloodied" they realize that they've "only" done half the dragon's HP, and are reminded that retreat is an option they can take. Remember that if the whole party decides to retreat, it can be good to drop out of combat, and make the attempted retreat a skill-based challenge, rather than trying to run the retreat on the combat grid. 5e makes it very very difficult for creatures to "outrun" other creatures that are trying to kill them, and the combat system doesn't handle retreating well.

If you want a mechanic for it, ask the player who wants to know to make a medicine check - this can add value to the medicine skill (which doesn't see a lot of play):

If they beat 10, you give them a very rough idea, like "they've been hit a couple of times but they look like they're going strong"

If they beat 15, give them a loose fraction to the closest 1/4 or so "they've lost about 1/4 of their HP" etc

If they beat 20, give them a number to the nearest 5 or 10 (depending on if you're low or high level.)

Increase these DCs by 5 if the monster is something that they'd be unfamiliar with the biology of - how easy is it to tell how hurt an air elemental is? not very.

An important thing to always remember is, every table is different, if one thing works for your group - do that, don't think that you have to follow any piece of advice just because it came from someone who sounded authoritative, or gave you a lot of numbers.

Usually not until they're below half or unless a player asks, I never give them the actual numbers though as I feel that would detract from the experience.

For me the players having a fun experienceb and building a character's story is more important than explicitly wargaming