Ever notice windows that seem disproportionately small in 16th and 17th century buildings? They're typically on the basement but can also be under the roof, occasionally between floors, or in a combination thereof. Well, those floors are servant's quarters.

All the buildings I linked above all date to the 16th and 17th centuries, and none are royal residences or otherwise palaces of government (although all are palaces of the highest aristocracy, only one or two rungs below the ruling dynasty, whose inhabitants would nonetheless be well-integrated in their highest affairs of state). All the palaces would have housed one or more branches of an important dynasty, as well as any hangers-on (Palazzo Durini, the last linked palace, hosted the Spanish Governor of Milan between 1662 and 1668 as a guest of its inhabitants, the Durini of Monza). All the examples I linked above are also in Italy, but I think trends in Italian architecture can be said to be sufficiently influential within the trends in the rest of Europe as to be broadly indicative of some universal patterns.

You allude correctly to an increased "professionalization" of servitude. In my area of interest (Italy — but also in the rest of Europe) you start to see a more marked differentiation between servant and retainer. In aristocratic homes of the 16th century, members of the extended family are increasingly divorced from household work, and this kind of work eventually becomes unequivocally the purview of lower-status individuals (which might nonetheless be tied to the head of the household in other ways: renters in the countryside might send some or all of their working-age children to work in the landlord's house in either town or country, for example) while in prior centuries there would have been a smaller gap in status between say, an extended family member tending the stables and an extended family member tending to the patriarch's investment ledgers (I'm not saying there would have been no gap at all, but the point is we are still discussing conditions of near-servitude that do not differ much between "varieties" of employment). This gap would instead become enormous over the course of the 16th century, with relatives only ever employed in privileged high-prestige positions (if they were "employed" at all, and not merely granted a stipend).

Likewise, the role of the aristocratic woman, and women in the aristocratic household, changed significantly: aristocratic women begin to take on a more managerial role within the household, with an ensuing clearer divide between servant and master. In other words, while in the 15th century many female extended family members in the household would be expected to be closely involved in performing domestic chores, the same tasks would be perceived as far below an aristocratic woman by the end of the 16th century. Indeed, by the 17h century aristocratic women might even be expected to manage both female and male servants in the household (I examined a specific category of male servant to aristocratic women, the Cavalier Servente, in this older answer which might interest you).

In all, this does indicate a changing conception of the aristocratic household. Servants are no longer close members of the family and are now employed for salary, rather than employed in exchange for privileges. As such they are not granted living quarters with the rest of the family, but must be housed in separate and possibly less-visible quarters (and this is largely true even in Royal Households, where some servant-type roles could still be acceptable or even desirable for aristocratic people).