At any pressure a human underwater is likely to experience (besides perhaps being immediately transported to the bottom of the Mariana Trench) it is not practic

At any pressure a human underwater is likely to experience (besides perhaps being immediately transported to the bottom of the Mariana Trench) it is not practically the fluid/blood that is being compressed but tissues and gases, so barring a barometer it would be difficult to tell this new haemogolobin to hit release. I’m sure you’re already are of the oxygen Haemoglobin dissociation Curve so O2-Hb release is already influenced by a number of forces that occur whilst holding your breath for ages (like increased CO2 causing decreased pH, increased DPG in oxygen poor tissues). What we would need is something that can carry a shit-ton more O2. So either a more efficient Hb molecule (could we get to 8 O2s?) or a way not to thicken a persons blood so much that they have a heart attack (the problem with just infusing more of the same stuff in)