Ok here's the idea: the character has to sleep and be rested. But how to implement this? With a sleeping pad and a parallel world called dreamland.

When you need to rest you put your sleeping pad down wherever you feel safe and go to sleep. When you sleep you enter dreamland. Dreamland is basically the same world, but slightly different. Food items aren't present in dreamland because you don't need to eat in dreamland. So all food items are made invisible and non-interactive locally for the dreamer (of course not global). When you enter dreamland you create a random character of yourself (same look, different stuff - sometimes you may have full military gear, other times just civilian stuff). It's basically you dreaming about yourself but in your dreams weird things happen, right? So instead of being a poor dude you're a high grade military officer for instance.

Anyways: you can't see or interact with nor hear other players who are not sleeping/in dreamland, but you can interact with those who are in dreamland. So dreamland basically turns certain things locally invisible and inaudible while it enables other things like fast travel and other gimmicks like maybe ghosting for some time - but only in dreamland. If you die in dreamland you wake up before your sleep cycle is over - as if you would wake up from a nightmare. But you don't lose any of the real gear you got because it was just a dream with dreamland-gear, right? As soon as a shot is fired in the real world nearby where you went to sleep you will abruptly wake up as well where you went to sleep. Either well rested or also like woken in shock - depending on how long you were able to rest.

In dreamland you can meet other people who are also in dreamland without having to fear they might "really" kill you on sight and take your stuff - because there is no stuff other than what you already have in dreamland - which is not lootable. But you can arrange a meeting with them in the "real world" if you feel you trust them through your encounter in dreamland - except for their skintone and face/gender they will be differently clothed and equipped. What you saw in dreamland of them was just their own projection of themselves at another time (or entirely fictitious altogether).

To make killings of the sleeping less likely:
If someone in the real world comes close to your sleeping self (1st "outer" perimeter, i.e. 200 meter radius from your sleeping body) it snaps you back to your real world body's location -weather you like it or not- but you remain still in dreamland! it is as if one of your senses is trying to keep you from harm and slightly waking you, but not quite. so while still in dreamland but on your body you are forced to look in the direction where the threat is (while they are still invisible because you are still sleeping after all). And you can't wake up unless they somehow wake you up either through being within the second, closer-proximity-radius (2nd "inner" perimeter, i.e. <100 meters) or they make noises (eating, shooting, talking, sprinting, reloading, ..) within this 2nd perimeters' radius/shooting within the 1st perimeter. You still can't see them from dreamland but you can see where the potential danger is coming from (through being forced to look in their direction from your sleeping spot while still in dreamland, after a quick snap-back to your body's location) though still asleep. So if the 2nd perimeter is breached you wake up, either well rested or abruptly and sweating as if awoken from a nightmare or shock (i.e. gunfire) after very little sleep, you then have the choice: pack your stuff and run away from the direction you were warned about or head towards that direction that you were forced to look towards in dreamland and confront the intruder. The choice is yours. But since you couldn't see the intruder(s) you might be up for a surprise - either good or bad.

Sleeping should give you the perk that you have better aim and maybe greater endurance in the real world. The other perks of being in dreamland, except from being able to meet new people without having to lose gear, are to be discovered and discussed.

I think all in all it might be better and more interesting than having tents. I would remove tents to be honest and include digging up crates for storage instead.

Oh and whether you sleep at day or at night is up to you - unless you haven't slept in a long time in which case you might not have an option. (Maybe daytime cycle should be cut shorter in order for this implementation to work - it's not like anyone is playing 24h without interruption, not to mention server restarts which resets the time back to the starting time - UNLESS the time will be persistent after a server restart, which could solve the time cycle issue).