Disclaimer: My area is more in the Early Modern than anything else, and more in England.

There are two parts to this. Firstly, it is worth noting the evolution in the concept, and importance, of privacy. Secondly, it depends on the circumstances.

Firstly, on the issue of privacy it is important to understand culture on privacy has changed. Historically speaking, privacy was more about who you talk to than being alone, it was more exclusiveness than solitude. So speaking privately with another person did not necessarily mean just you and them, and being alone with one person wasn't necessarily expected. There were many types of servants include guards and others that specifically attended in the private rooms like the Gentleman Pensioners in England. The Gentleman Pensioners were most prestigious than the Yeomen of the Guard, because as well as their usually higher birth, they were the more inner, intimate guards, less likely to be involved in common security incidents but more likely to be involved in the most important ones dealing with the monarch's personal safety. It was common for high-ranking household in Medieval and Early Modern Europe to have a servant or even a few servants on extra beds in a master bedroom. Letters tend to shared amongst the family household members and senior servants whenever it was not inappropriate or unwise to do so, and it was not uncommon for multiple copies of a letter to be produced and circulated to the households of other relatives.

Secondly, as you can see it does vary depending on what layer of exclusivity you are at, how able the people to even have many layers (this kind of privacy is easier when you have more layered, large households), and the particular circumstances. People may dismiss servants if they want to be particularly private, or go into a more private room. And conversely they can bring people in on things or go into a more socially open space. It's very modular.

Overall, it is definitely realistic that the high class were often in the company of someone at all times. They were rarely completely alone and many people around them, especially if you are a monarch or high minister, will be trying to see them and get their attention which limits their time to be more private. A key reason this was acceptable is not only was it variable and modular, but the people around you in the more exclusive environments were trusted. Even if by our standards having three servants there while you are having a very intimate conversation with your wife or an ambassador or whatever doesn't seem very private, if those people are part of your exclusive trusted circle that was private enough for them.