"Predator" vs "extremely intelligant" is a wierd dicotomy to make. Many mammallian predators are extremely intelligant, such as most canids, large bears, and felids.

On the other hand, sleeping is an energy conservation strategy for many niches. Obligate carnivores tend to sleep a lot, because its the best thing to conserve energy if you aren't activel hunting, ane the caloric payoff to a successful hunt is high enough that you don't need to spend all your time doing it.

Many leaf-eating mammals also spend a lot of time sleeping, and have even evolved extreme energy conservation measures, such as sloths having a unique muscle fiber arrangement and reversed wrist tendons

Most animals are just trying to conserve enough energy until their next meal since they haven't invented grocery stores yet. If that means they sleep between meals than that's what happens. Predators get that luxury. Prey animals sleeping all day is probably a bad idea.

Humans are also an outlier when it comes to energy conservation. Our bodies are ridiculously efficient but at the expense of not being very strong or fast. Endurance hunting is a thing humans can do. Instead of running faster than our prey we run longer than they can.

I'm not sure the amount of sleep is directly correlated with intelligence, and if it is I'd be also skeptical one directly influenced the other evolutionarily speaking.

To begin with, you have a very small pool of "very intelligent" animals, out of which humans outcompete all of them remarkably. So your sample size is an issue. Your second issue is how exactly you define and measure intelligence.

The amount of sleep is most likely an adaptation to various factors such as diet, amount of energy spent and needed, environmental pressures, etc.

Koalas sleep most hours of the day and trust me, they are not exactly smart or carnivorous. They sleep to preserve energy digesting, and they are not alone in this- snakes also nap after meals. As for cats and dogs, cats in particular are adapted to preserve energy. It's almost like their life motto. In the wild this allows them to go by without food for long stretches of time, very useful when you rely on prey availability.

I think carnivores only get to eat if they hunt something and tend to evolve in a way where moving around consumes a lot of energy since they need to be big/fast/etc

Dogs are omnivorous and so are we

It's not about intelligence, but about environmental pressures. I'd also argue that cats are more intelligent than many humans.