Modulo 32 congruences for Schur-type overpartition numbers

Let $S(n)$ denote the Schur-type overpartition function considered in the paper, and let $n$ be a nonnegative integer. Modulo 32 congruences. The following congruences are supported by computational evidence:

$$\begin{aligned} S(256n+123)&=S(4(64n+31)-1)\equiv S(64n+31)\pmod{32},\\ S(256n+171)&=S(4(64n+43)-1)\equiv S(64n+43)\pmod{32},\\ S(256n+235)&=S(4(64n+59)-1)\equiv S(64n+59)\pmod{32},\\ S(256n+251)&=S(4(64n+63)-1)\equiv S(64n+63)\pmod{32}. \end{aligned}$$

These congruences are presented as computationally supported directions for further work; the paper does not establish them, and their status remains open.