I must admit, I'm not at all familiar with what a federal republic, a federal state means, it seems to me like a very divided one. As far as I know, a monarch is an element of national unity, unlike the politicians, who are working under the "divide et impera" law.
I saw someone said that if monarchy was to be restored, you would have to choose a monarch in every Land, a "regional one". Please correct me if I understood it the wrong way.
I was rather thinking of maintaining the actual system, and only change the presidential institution with that of the constitutional monarchy.
You are a parlamentary republic anyway, the president does not have so much responsibility, the chancellor is the actual head of state. In this system, a monarch would have the role of unity and national pride ... as the tendentious ones would say, a "decorative" role.
You would only put the president's prerogatives in the monarch's responsibility. from what I understand, the chancellor chooses who is to be president, not the people by direct vote, so what would be there to lose?
We (I'm from Romania) have the problem of our communist past, that is still haunting us, there is still media propaganda, just in the old communist style, against the idea of monarchy. There is a stupid one that said, beginning with 1948, that the former king, Mihai I, would have gone abroad, exiled, with several railway carriages full of the "people's wealth, fortune" (this crazy idea is unfortunately still persisting in many people's minds, due to the decades of the propaganda), and another one, that is more recent, which says that by the act from 23 august 1944, he betrayed the marshal who was in alliance with the nazis (and the "interests of the nation") and that's why we, the romanians, had to live more than 40 years under the communists. As if the war could have eventually been won by the nazis! But of course, someone had to have the blame.
But still, now our king has a popularity and confidence of 42%, the highest since 1947, there are more and more of us who think that the restoration would be the only solution for our country, if we don't want to become like Russia or Belarus (you know, our president is much alike Putin).