I know that photon and gluon don't have any hypercharge so they can zip through higgs field at speed of light while left and right handed particles seems to communicate with these hypercharge, so then what do higgs boson really do?
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Hypercharge isn’t needed for the Higgs mechanism to work, it’s needed for Electroweak theory to match observations.
The Higgs mechanism can generate mass terms in a wide variety of theories, but the $\mathrm{SU(2)_L \times U(1)_Y}$ theory of the Standard Model is the simplest one so far that explains all the observations. As a specific example, if you know the ratio of the weak coupling to the electromagnetic coupling you can predict the ratio of the W and Z boson masses. As these ratios are consistent with the predictions of Electroweak theory containing hypercharge, it would be an astonishing coincidence if this were by chance.
Furthermore, it’s not quite true that all particles without hypercharge don’t have mass — the W and Z bosons don’t have hypercharge but interact with the Higgs via isospin (the SU(2) charge).
