> In my opinion, a mathematician does not know what the difference between "being literally" and "being encoded as" is

Wrong. The real numbers are literally a Dedekind-complete ordered field. The real numbers are encoded as Cauchy sequences, or as Dedekind cuts. Cauchy sequences are not Dedekind cuts: The former are equivalence classes of sequences. The latter are downward-closed sets without a greatest element. They are literally different objects.

Regarding your electron comment, the answer is straightforward: the electron is an excitation of the electron spinor field, nothing more. Fields are more fundamental than particles.