If that is the case would it be possible for those bosons to interact with other particles directly? Meaning the field associated with those bosons, interact with the field associated with other observables of other particles? (say, position, momentum, spin, etc.). Of course , this interactions should be limited, since limited effects had been observed.
I'm not sure how to undo the untold damage of popular science writing wispy metaphors, entrapping you to think along elusively absurd lines. From your careful wording I can see you are not involving the Higgs boson, soundly, but just the Higgs bosonic field, whose vacuum expectation value achieves three things through the symmetry realization it shapes.
It "gives" three gauge bosons a mass, leaving one massless, a popular way of summarizing how massive vector bosons are compatible with the chiral and weak isospin/hypercharge symmetries suggested by experimental data.
It "gives fermions a mass", which is a tortured way of saying that it keeps fermion mass terms gauge invariant, otherwise impossible for left-chiral lepton doublets.
It "gives" particles a charge by actually defining EM charge, through the ensuing Weak mixing angle.
Using mechanistic/anthropomorphic fantasy metaphors, beloved by complacent popular science writers (of the "just saying" school) you might argue that these masses are meted out by the same boson field (the Higgs boson being a remarkably inert observer in all this). In actuality, they are subtly interlinked pieces of the same mechanism.
The "cheat" in the above is that it is very hard to imagine neutral particles interacting with the Higgs field and picking up a charge in a notional relay race. (Don't even think about that. Don't think about lime-green elephants!) In point of fact, electromagnetism, and charge, are defined in this remarkably tight-fitting mechanism, at the heart of the genius of the SM. Now that we know this model works so well, we'd have some trouble thinking of the electric charge outside it, except in the context of a careful limit.