who used eunuchs to guard their harems.

Bear in mind this is kind of underselling the whole deal. If you live in a patrimonial state then the royal household is equivalent to the center of government. Relatives and close aides to the monarch are all influential, often serve in the administration and have the opportunity to accrue real power. Eunuchs guarding the harem means they are individuals who have access to all wings of the royal household, which is why they didn't just serve as guards or messengers or aides. Since the Ottomans often bought Eunuchs in the red sea, the chief black eunuchs were often in charge of religious endowments or vaqifs. Which means that they were in charge of some of the most important financial instruments in the empire.

It's like if the king of norway racistly believed that black ethiopians were the most courtly of peoples and bought an eunuch to administer a part of the country's sovereign wealth fund.