Small interactions in the groups $\mathrm{Sp}_4(q)$ for even $q$

The investigation of nonclassical interactions (orthogonality relations) in finite groups is continued. We obtain a description of all small interactions (small $D$-blocks and small $\Phi$-blocks) in the symplectic groups $\mathrm{Sp}_4(q)$ for even $q$. In particular, two known conjectures on these interactions are confirmed for these groups. Note that the existence of a small $D$-block in a group is equivalent to the existence of a pair of semiproportional rows in its character table and the existence of a small $\Phi$-block in a group is equivalent to the existence of a pair of semiproportional columns in its character table.