In that sort of situation, I take the offer, but as a way to return the courtesy, serve a second not a first. I just use it as a way to get a second shot at a second in case the delay causes me to miss the second.Fwiw I also won't take one that's offered in this situation. I just very much consider a ball rolling around the court in this scenario pretty normal, it's not like it's much further or more time than if it was served in the net and rolled at a skew into the doubles alley or something.
No one interrupted the court, no external factors happening, etc. Composure walking to pick up the ball then still hit your second serve is parta the second serve skillset imo