Is there a way to mitigate cohabitation that is inherent to semi-presidential system by making the unitary state look like a federal one that have only one federated state! I mean is it possible to split power between the president and the prime minister in the same way we do it between a the federal state and the federated one?
All in all, if it’s your country, it’s your constitution, you can define what you want.
In practice, I cannot see an arrangement of one higher entity (the federal state) and one lower one (the federated state) with exactly the same borders last long. In Germany, a federal republic, there are three city-states of which two (Hamburg and Berlin) are composed of exactly one city. In these city-states, the elected parliament functions as both a state parliament (like in the states of Brandenburg or Schleswig-Holstein) and a city council (like for the cities of Potsdam or Lübeck – all examples chosen for proximity to Berlin or Hamburg). The chief elected official is termed ruling mayor (Regierender Bürgermeister), the title of which puts him on par with other mayors but at the same time he is also on the same level as the minister presidents of the other states. Depending on which conference he is in he will be either or the other. The parliaments of Hamburg and Berlin enact legislation equivalent to other cities and to other states depending on the subject at hand.
I would strongly assume that any one-state-federation would reduce itself to such a structure—which essentially is just a sovereign state without subdivisions—sooner or later if only for saving money.
As for the balance of powers between a prime minister and a president: there are numerous ways to achieve that without the need to introduce a pseudo-federation.
Technically I don't see any contradiction in such a system, but this would require a very clear definition of the area of competence for these two representatives of the executive branch. For example one would be responsible for foreign affairs, defense and security while the other would take care of healthcare, education and agriculture. It would probably require two independent budgets and resources, otherwise the one which holds the financial power has a lot of leverage on the other.