The $K_{2,d}$-free path conjecture for tree-independence number

For positive integers $d$ and $s$, a graph is $\{K_{2,d},P_s\}$-free if it has no induced subgraph isomorphic to $K_{2,d}$ or the $s$-vertex path $P_s$. The $K_{2,d}$-and-path conjecture. For any two positive integers $d$ and $s$, the class of $\{K_{2,d},P_s\}$-free graphs has bounded tree-independence number. This is posed as a weakening of the previously stated biclique-and-path conjecture; the source presents it as an open direction.