a meditative state is definitely helpful in reducing the body's consumption of oxygen.
I got my open water scuba certification many years ago from a former Navy SEAL.
At the time, I was 4' 8" and weighed 85 pounds.
The Navy SEAL was about 5' 10", 200 pounds.
Every single dive we went on he used less than half the air that I used, and I used less air than the rest of the dive group (because I didn't need as much given my stature).
He explained that he used a meditative style breathing pattern and simply remained very calm underwater.
Your incorrect assumption is that you're supporting the same hardware with different software.
Drastic changes occur with aerobic training and hypoxic stress in the red blood cell count & blood volume, blood pressure, heart stroke volume & lower resting heartrate. He has more muscles, more energy stored in glycogen in those muscles, and swims faster. The person you learned from was likely not physiologically capable of long dives when he first started, no matter his mentality. And nobody is capable of using a "meditative breathing pattern" while they're exerting themselves at the limit of their aerobic capabilities; He was farther from them than you were. There are likely other long-term adaptations we don't know about, specific to diving.
He was quite a bit more physically fit and obviously he was an adult (and a former Navy SEAL) and I was a teenager, so yes he had quite the physiological edge on me.
However, part of what he taught us was that when diving, with our without SCUBA gear, one shouldn't anywhere near approach the limit of one's aerobic capabilities, for precisely the reason of conserving one's air supply (and, honestly to focus on the experience of the dive and the amazing ecosystem around you).
I got much better at reducing my use of air by the time I got my open water cert, but I still never got anywhere near to how little he used.
I had the same experience. My first 5 or so dives, I was burning through air like crazy. I also had some pretty serious underwater-anxiety that I was dealing with. I spent some time just hanging out underwater without scuba gear, basically doing ~30 second underwater meditation to help the anxiety go away and to practice controlling my breathing, and my air consumption went way down, plus diving is way more fun when you're super relaxed and just moving around using the most minimal motions to propel yourself.
I got my open water scuba certification many years ago from a former Navy SEAL.
At the time, I was 4' 8" and weighed 85 pounds.
The Navy SEAL was about 5' 10", 200 pounds.
Every single dive we went on he used less than half the air that I used, and I used less air than the rest of the dive group (because I didn't need as much given my stature).
He explained that he used a meditative style breathing pattern and simply remained very calm underwater.
/anecdata