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The difference between display and real world will be at most slight to a trichromat, while it would be extraordinarily obvious to a tetrachromat.

It's not very uncommon for people to be colour blind, dichromats. If media on screens would be dichromatic while the world around me is trichromatic, I would certainly notice at once.

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I suggest trying to quantify "extraordinarily", using the actual spectral response curve for the tetrachromat's fourth cone, called "Q" in the paper shared by varunneal. Most people casually equate the short (S), medium (M), and long (L) cones with blue, green, and red, with the idea that these are all as different as can be, but the M and L cones are very similar to each other, compared to S. The L, M, S curves are independent but far from orthogonal in the way you may be thinking as you say "extraordinarily". The Q curve is just another wide bump, with a peak in between that of M and L, so again, very far from being orthogonal. Whatever 4th dimension of color perception is accessed by the Q curve, it is a relatively cramped dimension, so reliably detecting perception along it requires some carefully designed stimuli.

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