This is not exactly what you asked, but if I were pouring out my heart in a close conversation with my husband and someone entered the area, like say the guy fixing my furnace, I’d either stop talking or I’d switch to a less heartfelt level of discourse. I’d probably acknowledge the other person and interact with them as well. I’d alter my communication patterns, in other words.
I am like you, though, and I will stop certain types of prayer if someone enters the room. Not if it is a short thing like grace, but if I am feeling close to God and meditating, I will lose that sense immediately. It wouldn’t happen if I were in a large chapel, with the understanding that everyone is directed towards the tabernacle. It would happen at home, where whomever wanders in the room might well want my attention.