Is there any kind of “sleep” cycle that occurs for transitioning souls stuck in limbo? What about dark spirits and even angels? Is anything like sleep engaged in or needed? What about light beings in the divine realm, do they sleep?

Transitioning spirits do not need sleep physiologically. They are in a different state energetically and are existing through life force energy conveyed to them on a direct basis from the divine realm to keep them going. Lacking a physical body, there are no physical needs for replenishment or clearance of waste products, and so on. The spirit form is a more simplified and pristine state of being in that it is more a level of vibration experienced by consciousness itself and needs some sustaining energy to maintain its existence, but it is not akin to the physical body and all of its varied physical needs. The problem with being in limbo is being present in a vast nothingness and out of touch with prior life environmental cues and the workings of the body as a housing that one is quite used to but not used to being a free-floating consciousness in the vast nothingness of the lower astral plane. This isolation can become quite stultifying and even a source of terror. It is quite akin to being buried alive where nothing moves, there are no sounds or sensations and one is simply feeling suffocated, unable to experience anything because one is essentially trapped in a dark void. This can be a source of torment and then when spirits are set upon by the dark spirit meddler cohort of fallen angelics, who seek to cause harm to other beings and draw energy from them in a selfish pursuit to maintain their own survival, they will savage any hapless earthbound human spirit and torment them because they know they will summon greater energy, and that serves these parasites. So it can be a brutal existence that will go on constantly with no let-up. Under such conditions, sleep would be a blessing indeed, but they cannot escape it. Similarly, the dark spirit meddlers and the angelics who are in divine alignment do not need sleep either. The spirit meddlers have a tougher time because they need an external source of energy to keep going and may become relatively quiescent through exhaustion because too long a time has passed without an energetic source they can prey upon and draw energy for themselves as a parasite. The true angelics in divine alignment, like human beings, are tapped into the divine and will draw life force energy to preserve and maintain their consciousness indefinitely and have all the energy they need and have no need for sleep whatsoever because their awareness does not depend in any way on the workings of a physical body with a brain that becomes fatigued after a time and will begin to have fuzzy thinking, a fog-like state of fatigue, and even delusions and hallucinations if pushed too hard for too long without a rest period to clear away cellular by-products of the furious mental activity that is typical of the waking state. Light beings in the higher astral plane, the heavenly realms, do not sleep either, and that again is because they are in a high vibrational energetic state with unlimited sources of pure energy at their disposal and it is in a sense an effortless existence because energy can come and go to be deployed in various ways through the consciousness of the being without inefficiency or waste products being produced that could result in any kind of diminishment or impairment as happens with metabolic processes in the physical organism. So light beings can work and play with no let-up and no fatigue. This is a blessing indeed and accounts for the tremendous progress and gains made by light beings in the higher realms and the higher vibrational beings in existence on the higher planes of existence. This is the destiny for humanity to reach when you are ready as a result of healing the interlopers standing in your way and then yourselves, to repair the many karmic woundings inflicted on you.