The note on Genius says that one does not usually interrupt the King. It is not polite. It is not wise for a subject to interrupt his King. This explains a) why kings tend to be so maddeningly long – winded and b) why Claudius is such a jerk to Laertes in the next line.
I wonder if Claudius benefited from his proximity to the King before he was king and learned his longwindedness at his brother’s side, or did he watch his brother ramble on and on and it was this privilege of his that he envied the most, perhaps talking without interruption was his big dream and so when Laertes does it…it really rankles.
The privilege to not be interrupted is definitely enviable. Women know this well. And men who are interrupted by women respond with so much rancor as Claudius. See also Jeff Sessions questioned by Senator Kamala Harris.