The Italian ambassadors from Venice and France, he notes, often provided updates on the sexual favourite of the sultan among the Janissaries. He also infers the court was very liberal and tolerant sexually. What I didn't understand properly is if this was specific to a period or a single sultan, or typical of the culture of the Ottoman court. .
What do we know about the sexual liberties at the Ottoman court? Were they comparable to the French court, for example?
I would caution against the term "liberal". As you move away from the 21st-century West into other periods and cultures, sexual mores do not neatly line up on a line from conservative to liberal as we define the terms. It is true though that the sexual mores in the Islamic Middle East before modernity were different from what 21st century Westerners - whether liberal or conservative - adhere to.
There were indeed same-sex sexual relationships, but they were not homosexual in the sense that term is meant today. The distinction they drew was between penetrator and penetratee. A fully grown man was in the role of penetrator, and a woman or boy/youth was in the role of penetratee. There is no evidence that they had a concept of "heterosexuality/homosexuality" as exists in the modern West, where you are in one category if you prefer a male partner and in another category if you prefer a female partner.
I am not familiar with the Ottoman court specifically, but these sorts of relationships were generally widespread in the Islamic Middle East going back centuries, at least among the elites. It's a common motif in Arabic and Persian poetry - the charms of the beardless [male] youth. There are numerous mentions in the sources of slaveowners using both male and female slaves in this way. How widespread it was I don't know, but it was often remarked upon, with authors saying things like, "such-and-such elite does not have a predilection for beardless youths, as is usual for men in his position." And there are reports, when a city was conquered in war, of the women and the children of both sexes being distributed among the victorious troops along with the rest of the loot of the city.
Also beauty was not marked for gender the way it is in the modern West. Whereas we treat beauty as something specifically feminine, in premodern Arabic and Persian poetry, both women and young men could be beautiful. In fact, come to think of it, it seems like most of the love poetry talks about a male beloved, but I could be mistaken. There is sometimes a bittersweet tone to a lot of this poetry. It'll talk about the comely features of the beloved, and also the sadness knowing that soon his beard will come in, which will make him no longer desirable. His peak of desirability was when he was getting some peach fuzz on his upper lip, but that's also of course when he's about to start growing whiskers.
A couple books to read about this:
Khaled El-Rouayheb, Before Homosexuality in the Arab-Islamic World, 1500-1800 (Chicago: University of Chicago Press, 2005)
Afsaneh Najmabadi, Women with Mustaches and Men without Beards: Gender and Sexual Anxieties of Iranian Modernity (Berkeley: University of California Press, 2005). This is about Qajar Persia rather than the Ottomans, but there's a lot of interesting social history here.