However, for trumpet players it is more important to deliver the gas (oxygen) than to store it (increased inspiratory volume).
From Physiology, Residual Volume
John J. Lofrese; Connor Tupper; Deanna Denault; Sarah L. Lappin. October 20, 2021.Copyright
2022, StatPearls Publishing LLC.
"Following maximal inspiration, the volume of air that leaves the lungs during a maximal force expiration is known as the vital capacity (VC). VC is composed of the tidal volume, expiratory reserve volume (ERV), and inspiratory reserve volume (IRV). The ERV is the volume of air that can be forcefully exhaled after a normal resting expiration, leaving only the RV in the lungs. Forcefully exhaling the ERV is an active process requiring the contraction of expiratory muscles in the chest and abdomen."
So the key to enhanced trumpet dynamics involving air flow when moving the air from the lungs to the mouth involves more the contraction of expiratory chest and abdominal muscle. This is why I would recommend more using a weight lifting routine focusing on building expiratory respiratory muscles of the chest and abdomen to enhance "air delivery" for brass players as opposed to "air supply".
I have developed a series of 9 sets of exercises that enhance chest muscle function and 6 exercises performing 15 reps of each set of exercises, that enhance abdominal muscle function on my Bowflex system. I do this 40 minute work out every morning and it has done wonders to increase my trumpet playing endurance.