According to empirical evidence, how do sleep and dreaming play an important role in supporting cognitive performance in such areas as learning, memory, and cognition?

According to many empirical studies, sleep and dreaming do play important roles in supporting cognition functions such as learning, memory, and cognition.
First, learning and memory involves three functions. The first is acquisition, when the brain acquires new information. The second is consolidation, which refers to the process of retaining the new information. And, of course, the third is recall, which refers to our ability to access the stored information.
Studies suggest that REM sleep is especially crucial for retaining declarative memory. Essentially, declarative memory involves the acquiring of facts and/or knowledge. This type of declarative memory is also known as semantic memory.
Declarative memory differs from procedural memory, which encompasses skills that we learn. The acquiring of skill sets contributes to episodic memory. Sleep, as many of us know, is composed of REM (rapid eye movement) and non-REM sleep (which is further divided into three stages). In previous decades, non-REM sleep was divided into four stages, but modern scientists have since consolidated Stages 3 & 4 into one stage. The last stage, N3, is typically referred to as slow wave sleep (SWS), which facilitates the retention of declarative memory.
Meanwhile, REM sleep facilitates the retention of non-declarative (or procedural) memory. The double-step process of REM and SWS helps us consolidate memory. Again, consolidation is the process of retaining new information we acquire during our waking hours.
Studies suggest that non-REM sleep (and especially Stage 3 SWS sleep) facilitates the recall of factual information. Please refer to the links below for this info. Certainly, sleep serves two functions that promote learning, memory, and cognition: consolidation and restoration.
As for the restorative function, neurotoxic waste products are removed from the brain during sleep. When we sleep, cerebrospinal fluid freely circulates in our brain, removing waste proteins such as β-amyloid (Aβ) (8), α-synuclein (9), and tau(10) from the interstitial space. So, sleep is both restorative and consolidative in function.
https://therapeuticliteracycenter.com/the-role-of-sleep-in-learning-memory-and-health/