@breizh Late reply here. I know you're not being too serious with these criticisms, but I wanted to mend your suspension of disbelief a little as that may help you to enjoy the series.
As you said, this is a manga, so it isn't exactly realistic. However, this series actually makes a lot of sense.
1) Feeling sleepy in the afternoon (which is when 5th period is, A.K.A. Saeki sleep time), is common to most people. Through various natural processes within your body, melatonin is released around this time, making you want to sleep.
2) You say that she would have a hard time in Japanese society, and maybe she would. However, study after study actually shows marked increases in productivity after napping, making workers more efficient. If an employer were smart, they would allow afternoon naps for all employees if possible. Also, note the tradition of the siesta or similar concepts that exist in many cultures around the world, which indicates that this has been understood to some degree or other throughout human history. Now, it's true that Japanese companies aren't exactly the most progressive, so it's doubtful they would implement such a policy. However, much of the time Japanese spend at work is merely to look busy so you don't look lazy, not spent doing actual work. Therefore, with Saeki's skills, she could probably take a nap while making people think shes awake, similarly to how she does things now, and still get all her work done on time -- actually probably faster than other people given the productivity boost.
3) As for the steamed bun making her sleepy, food does often seem to induce sleepiness, though we don't completely understand why. This is particularly true in the case of carbohydrates, which the bun appears to consist largely of. One theory is that carbs increase the uptake of tryptophan from food, which is related to the production of serotonin. Serotonin, in turn, is the precursor to melatonin, hence it induces sleep. Another theory that may hold concurrently true, is that the simple carbs you find in foods like the aforementioned steamed bun (probably), are simple sugars. These cause a quick increase in blood sugar, followed, inevitably, by a drop, resulting in tiredness. And yes, it probably hit Saeki way too fast, but maybe she has a high metabolism. Also, it's a manga, so yeah.
4) Lack of physical activity, like sitting in a classroom for long periods, results in there being very little going on in your body to counter these effects, and may in fact encourage your body to enter a lower energy state that tends toward being sleepy. I would wager many of the people here have felt sleepy at some point during class at least a few times, if not nearly every school day ever (like me).
Further reading/sources:
https://www.apa.org/monitor/2016/07-08/naps
https://www.medicalnewstoday.com/articles/323379.php#how-to-stop-feeling-tired-after-eating
https://www.sleep.org/articles/reasons-for-afternoon-slump/
As you can hopefully see, Saeki is actually a fairly normal human being, just taken a little further to the point of comedy. I hope this information will further your enjoyment of this series, 'cause I love the hell out of it. I hope you've enjoyed it thus far regardless, and thanks for reading!