What is left in our lungs when we are literally out of breath (not dead) , and why taking in the atmospheric air makes us float in water ?

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Let me try to elaborate,

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what gas (i am assuming low pressure than atmospheric air) is left/replaced in our lungs in the scenario when we are out of air say underwater or someone consciously expels every possible breath for a short while?

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i mean it cant be vaccum or oxygen, surely it is something

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and why does taking in the atmospheric air ( i guess having more mass than this "gas" ) makes us float in water while opposite makes us sink ? isnt the phenomenon opposite to that? or am i tripping?

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reason i think this "gas" has a lower pressure hence lower density/mass than atmospheric air,

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a) we would have to expel it while breathing and,

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b) we would have to intake it again while throwing out co2

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c) we would exert a significant force doing that

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all of which doesn't happen in quick manual tests