You're title seems to better reflect what I think you're asking
You're not concerned about rest; you're concerned about regaining resources
So given that a party is locked up for 8 hours, how do you prevent them from being back at full strength when it's over?
There are a number of features that allow party members to recover some resources given a "short rest":
- Hit points via using hit die
- Warlock spell slots
- Monk ki points
- Bardic Inspiration (after 5th level)
- Cleric Channel Divinity
- Wizard Arcane Recovery
- Druid Wild Shape
- And many more
So given even just an hour of alone time, there are a number of resources that a party can replenish. But not everything; other than Warlock, most all spell casters only get back all of their spell slots after a long rest. A Barbarian doesn't recover Rage without a full rest. And so on.
So what the party can do with a short rest depends entirely on the party makeup
Even stripped of their equipment, most of the short rest features will still work. So while the Wizard cannot do Arcane Recovery, the Warlock still get back their slots.
So regardless of the method used, if the party is allowed a short rest, they can still be a force to reckon with. Or they can just spend their time licking their wounds and hope an opportunity to escape presents itself.
So how do you stop/limit people from getting a short rest?
The obvious way would be to have guards stationed nearby that would prevent the party from relaxing. But even then, that borders on torture which may trigger players and doesn't seem like fun game play.
My suggestion; don't.
Let the characters get their short rest but not a long rest. Have the guards wake them up every other hour for whatever reason.
And when the morning comes, have the guards ready to handle the characters--Dispel Magic, Charm Person, Command, handcuffs, blindfolds, what have you.
If you make up some rule saying the players cannot use the abilities of their characters, then you are taking away their agency. Build the story around what is possible; don't change the rules to fit your story.