@Just_Victor ~ I'm not qualified to comment on all of what @Victoria33 mentioned, but agree with the following:
Personal story, if you will: our daughter had a HS water polo coach who barely slept, and he was unbearable. The team was comprised of enough good players to win most matches with proper coaching. Our daughter was told [by a competing coach] she and another were scholarship material. Anyway, the coach would allow the girls to get to a lead [of one goal or two], and then during the last couple of minutes, he would take out a starter and put in a bench player [one of the overweight girls who was slow because of her lack of fitness]. The girls would be screaming to try to win [the parents were aghast!], but could not hold on [against an ultra-competitive team] and would lose. The team would sit on the bleachers after the game with tears running down their faces while the coach would say, "You just didn't play hard enough."
As time went on, this coach was no longer employed by the school, and the assistant coach [wrote me an email and] eventually admitted to me the coach-who-didn't-sleep-at-night told him he threw the games, just because he wanted to see how hard the [out-of-shape] girls on the bench would fight in a stressful match. Not enough sleep impairs common sense thinking, and makes one cruel to boot.
[I'm glad Mike Pence accepted VP.]
I think sleep deprivation affects different people differently, but here goes.
In my work, I have had occasion to (once) work an entire week with 8 hours of sleep. Not eight hours of sleep a night, but eight hours total sleep for the week. I knew I was not going to get much sleep, the situation was unavoidable, and decided to make note of my reaction to the inevitable sleep deprivation. I was living on the drilling location, the only geologist present, and no other was on the way. At any time in a day I could be called on for steering decisions (an early Bakken Horizontal well, one of the first in the latest boom), and worked a scheduled 12 hour day monitoring gas detection equipment and describing drill samples.
First I noted the expected physical fatigue and loss of mental sharpness. Irritability increased for a while, then tapered off as I resigned myself to not getting meaningful sleep.
Sleep did become an obsession for a while, but the obsession part and much of the irritability is optional, brought about by focusing on the sleep I wasn't getting instead of the tasks at hand. Deciding you are not going to get that sleep, do not have to have that sleep, and realizing your performance will be degraded while figuring out how to keep that from affecting the final result is key to functioning at all, but being resigned to not getting the sleep reduces irritability considerably. It is what it is.
After a couple of days of this, performance degraded.
Calculations had to be checked twice, and in fact before long I was double checking pretty much everything. Decisions came more slowly, and indecision increased as longer trains of thought became progressively more difficult. The tendency to have difficulty relating logical processes to others was noted first, and then the degraded ability to perform those processes. With that came the tendency to offer solutions without explanation, and as this was a prototype operation, that was not optimal performance.
However, prior explanations of analogous situations during this project often provided logical examples which could be referred to, and this helped considerably.
I would say the ability to get anything done was down by as much as 50%, partly due ti double checking everything and indecision brought on by difficulty focusing on more complex tasks. A 'power nap' of as little as 15 minutes would make a significant difference, for a while.
Some parts of the job had been reduced by years of experience and repetition of the process to nearly automatic: there was already an existing mental template for describing drill cuttings, for instance, and these tasks presented the least difficulty.
This degraded level of performance plateaued, but any opportunity to catch a nap, no matter how short, was used. I found myself taking 'micro-nods', involuntary dozing for no more than a few seconds. These would continue off and on for an hour or two until some necessary level had been obtained, and then there would be periods of continuing on without such incidents. I avoided physically hazardous situations at that point, for my safety and the safety of others. I 'nodded off' while remaining standing on a few occasions, two of which were observed by others. When those involuntary nap episodes happened, or other distractions, I had to reorient afterwards as to what had been done before proceeding (everything was documented, that was part of the job), which became a significant part of the inefficiency the lack of sleep imposed.
The work involved the microscopic examination of geological samples, and I awoke a couple of times at the microscope, with the eye cups around the lenses supporting my head, having dozed off for a couple of minutes.
Short term memory suffered notably, while long term memory was intact although I was often left groping for words. To compensate for the former, I started writing everything down so I had a record.
By the end of that week, I was hearing sounds, including voices or music which had no apparent source, and could 'call up' songs like listening to a MP3 player. Admittedly, the repertoire was limited, and understanding there was no one in the room or with that voice present nor any radio or source for the music enabled me to write the effect off to lack of sleep.
Another side effect was a degree of paranoia. In my case, malfunctioning mechanical or other devices were credited with human attributes, as in: "That switch doesn't like me", just a short stroke from 'That switch is out to get me', and not too far from the desire to "get the switch first, before it messes with me again". Fascinating. Recognizing on a intellectual level that that switch was just a thing, devoid of harboring feelings of malice or caring one way or another, was important, but the tendency was noted.
I fully and successfully resisted applying that line of thought to humans, as we were all working toward the same goal, but can see where in different circumstances someone sleep-deprived might well become suspicious of the actions and motives of others, especially people they might have a reason to distrust or suspect of malice in the first place (like a meth head with police, for instance, where agitation as an effect of the drug coupled with paranoia from lack of sleep could have undesirable results for both).
Another strange manifestation of sleep deprivation was the tendency to make meaningless adjustments in the position of equipment or supplies, moving something a few inches, then moving it back shortly afterward, without any advantage to the movement either way.
At the end of the week, the job done under what thankfully proved to be unique circumstances, I slept for 24 hours straight, and took about a week to get back up to normal performance levels.
I believe a person can perform some tasks with little sleep for extended periods, in certain circumstances where necessary functions are well enough ingrained as to be pretty much automatic, and paranoia can be a plus (line troops), with the proper mental safeguards against making basic mistakes.
That does not include interacting with a lot of people under novel circumstances, nor making decisions not based on cut and dried parameters which can be established beforehand (mechanical or other quantifiable limits). The probability of errors in judgement in complex situations, especially the synthesis of solutions to novel crises is severely degraded, and that effect may be further enhanced by irrational feelings toward persons or equipment. Seeing or hearing things which are not present, or attribution of situations to malice on the part of others or inanimate objects is a clear risk.
At some point, the brain will rest, even for short moments, and acquire a minimum level of that rest whether the person desires that or not. The immediate effect of that involuntary rest is performance degradation, but can lead to missing critical data needed to make informed decisions. In my case, everything was recorded and could be reviewed, but in many instances, that would not be the case.
Paying attention to the effects was a bit like making lemonade out of lemons. The situation was not one which would have ordinarily been intentional, and I only took advantage of an opportunity to learn about the effects of a situation I would not ordinarily have been in. My decisions were pretty cut and dried, despite some broad aspects of the situation being new and different for almost everyone involved. I cannot imagine dealing with the scope and variety of decisions which would be necessary as POTUS under similar circumstance.