Bulky tanks aren't only needed for air, they are needed for pressure. Human diaphragms are not strong enough to pull air into a lung against the pressure of the surrounding water at depth. Scuba regulators blow air into the lungs at a pressure that is just a tiny bit above the water pressure. Furthermore, oxygen itself can be toxic if it is breathed at high pressure. Divers breathe a mixture of gases such as air which is mostly nitrogen with a smaller fraction of oxygen or a helium-oxygen mixture.

this article is fundamentally vague and as such misleading.
adsorptive materials are use for filtering gasses from gasses and must remain under pressure.
the allusion/implication that this material can filter dissolved oxygen from salt water, let alone fresh water into an adsorptive material which can then release the o2 as a gas, seems purposefully vague as to make this article click bait [garbage].
most likely this 'discovery' is simply another high adsorbtive material. which might have the potential to condense the volume of air into a smaller tank, without much changing the overal weight.

Breathing pure O2 at a depth beyond about 30 feet leads inevitably to blackouts, convulsions, and without a bit of luck, death.
The "bucket" would need a tank of an inert gas to maintain a proper partial pressure. And that would lead to a rebreather as most of the requirements would have been met.

Another sci-fi device that will become a reality. Just like in some sci-fi movies where they pull out the little "breather" device no bigger than a co2 cartridge that they hold directly with there mouth and never runs out of air.

How heavy is it per oxygen contained compared to say a 20 Cubic Ft. Oxygen Cylinder?
Does it efficiently strip oxygen from hydrogen?

this is both an awesome improvement and a weapon.

Seems like there could be unique applications for this in space flight. Storage of oxogen without using pressure and its assosiated weight (the container) or safety issues. Call NASA. They have money to burn.

Every year we see amazing inventions such as this, and they are never seen again.

Sounds interesting but pure oxygen is poison at depths below 33 feet. There is also the problem of re-breathing the exhaled CO2 which would have to be scrubbed out. What gas will be the filler? Nitrogen to 100 feet and helium for deeper dives? This is a lot more complex than it looks at first glance. Due to the controls and regulation that will be required, it probably won't be nearly as portable as it sounds. For people that need oxygen for medical purposes, oxygen concentrators have become a lot more portable but they make noise and require a power source. If this material releases the oxygen using a little heat or vacuum, there may be a lot of options possible. Recharging the system also brings up more questions. Will it recharge itself by simply opening up the container and absorbing oxygen from the atmosphere or will it require special equipment?

Space Travel ??