Self-explanatory. Did any royal court in history from ancient to medieval times (of any culture) have a public restroom that people who attended court can use, or were they sort of left to their own fate, and destined to leave court for a long period or make a fool out of themselves? I suspect time spent at courts were of multiple hours.
Tycho Brahe was not exactly a courtier, but he had to court the emperor who was sponsoring Tycho's research. In October 1601 he attended a banquet with the emperor (Rudolf II) and what happened was described by Kepler (I cite from Wikipedia):
Tycho suddenly contracted a bladder or kidney ailment after attending a banquet in Prague, and died eleven days later, on 24 October 1601, at the age of 54. According to Kepler's first-hand account, Tycho had refused to leave the banquet to relieve himself because it would have been a breach of etiquette. After he returned home, he was no longer able to urinate, except eventually in very small quantities and with excruciating pain.
Remark. On the other hand, Louis XIV was known for giving audiences to his courtiers while sitting on a chamber pot.
Novels I have read that take place during the time period 1783-1815 (Roger Brook from Dennis Wheatley) mentioned that dining rooms often had a curtained off area, where a Chamber pot was situated that men would use to avoid the inconvenience of leaving the room.
Women would go to a special room to 'powder their nose' (what that term actually meant was never fully disclosed).
No mention of how servants dealt with the problem, but assume that they also had chamber pots available somewhere where people of 'quality' would not go to.
I remember going on a tour of Hampton Court in England many years ago. The docent said that as guests supped at the table, they would just open up whatever covered them and let it go right under the table everyone was eating at. These would have been male guests, presumably. I know ladies used the bour de leau (spelling?) which was shaped like a modern gravy boat and fit up under their many long skirts with the assistance of a lady's maid.
I also read (many years ago) in Nancy Mitford's book on Louis XIV that he did not like to be at all aware of anyone's biological functions (especially women's.) This made going on a long trip with him particularly difficult. I believe Mitford recounts a specific story in the book. The Sun King: Louis XIV at Versailles.