On the conjecture about semiproportional characters in the groups $\mathrm{Sp}_4(q)$

Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters $\varphi$ and $\psi$, then $\varphi(1)=\psi(1)$. In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for the symplectic groups $\mathrm{Sp}_4(q)$ and $\mathrm{PSp}_4(q)$.