This is in contrast with other breathing exercises to do cause an actual build up of CO2 to levels well above what feel normal. Freedivers call these CO2 tables and they’re used to build CO2 resistance and increase breath-hold times.
https://www.wimhofmethod.com/breathing-exercises
“When we breathe in, we take up oxygen and release carbon dioxide from our blood. Our blood is usually already fully saturated with oxygen (about 99% saturation) and breathing deeply does not raise that saturation. Breathing deeply does, however, release a lot of carbon dioxide. This, in turn, lowers the “urge to breathe”.
The brain stem, specifically the pons and medulla oblongata, is sensitive to carbon dioxide. Having too much carbon dioxide in the blood will trigger your brain stem to breathe. By removing carbon dioxide from the blood through deep breathing, this impulse to breathe from the brain stem is lowered.
In short, the lower the level of carbon dioxide, the longer you can hold your breath. The impulse is just not triggered yet.“
Are we talking about the same numbers as a (calibrated) O2 optical saturation monitor reports or something else?
Blood O2 and CO2 percentages don't sum to 100%. O2 saturation refers to the percentage of hemoglobin molecules which have oxygen bound. Only some CO2 is transported bound to hemoglobin.
If you intentionally breath deeply, greater than tidal volume, it means at the same breathing rate, you are exchanging more air in total and will be purging more CO2 than you produce which will lead to hypocapnia over time.
Hypocapnia doesn't inherently need to result from deep breathing if you offset the greater-than-tidal volume with less-than-normal breath rate — if you are breathing very slow or 'skip' breathing with pauses in between, but that balance can be pretty hard to reach