[sigy]

The divers can not inflate it further once submerged, yet have put their mouths on the container.

Even as a "re-breathing" container, having that reserve of air volume would allow for extended lingering time below the surface, as it would take much longer for the CO2 saturation to become a problem than just a lung full of air.

Thus, this likely served two purposes. 1) buoyancy to counter the weight of armor, and 2) additional time underwater by rebreathing (more) stale air than one can hold in their lungs.

Think about it, what would you do?