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> Heat lost to the water (maybe half of the energy input to compressed air) could be reclaimed as the pressure is released, with simple heat exchangers.

Heat lost to the water is lost. If you want to try to avoid that you need to save that heat energy after the compression stage.

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I see that you have not thought this through. Yes, some of the heat will not be recoverable, but controlled expansion of highly pressurized air creates a large temperature drop that would readily absorb heat from the ambient water.

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