The Higgs mechanism has been theorized to give mass to elementary particles [1]. That is not to say that the total of inertial mass of a non-elementary massive object is due to the Higgs Boson.
References“Higgs Mechanism”. Accessed: 2024-08-13T07:13Z. Wikipedia. en.wikipedia.org/wiki/Higgs_mechanism> the Higgs mechanism is essential to explain the generation mechanism of the property “mass” for gauge bosons.