The diagonal magnitude homology conjecture for triangles attached to a square

Let $C_3$ and $C_4$ denote cycle graphs of lengths three and four, respectively. Form a graph by gluing two copies of $C_3$ along single edges to a single copy of $C_4$, and suppose the two triangles are not attached to opposite sides of the $4$-cycle. Triangle-square gluing conjecture. The resulting graph has diagonal magnitude homology. This is supported by the computations described in the source, but no proof or resolution is given there.