The medical/psychological term for this excess of stimulus is 'over-attending.' Your brain get overwhelmed trying to attend to too much at the same time.

You threshold will vary from day to day, depending on things like sleep deprivation, physical effort, sensory stimuli, pro or con nutrition, etc. It is very worthwhile to use simple empirical science to observe the many factors that precede an over-attending episode. You will likely find the overlaps form event to event and learn to moderate these factors.

I like you term 'ambient processing threshold.' I know that if I am in a setting with multiple people talking, eventually, I will walk away from the group to a quieter area. I do not even need to be paying attention to the voices. My brain will hit its threshold either way.

People, even professionals, fail to understand how we can become overwhelmed by the ambient noise in a room. Maybe we need to try to ask them how they feel when they are at the theater and someone behind them is talking on and on. Eventually, even the most patient person will become unable to follow the dialogue on the stage or screen. We live with this 24/7.