Parametrised loop coproduct obstruction conjecture

Let $E\to B$ be a smooth fiber bundle with fiber a smooth closed manifold $M$, and let $f:E\to M\times B$ be a fiberwise homotopy equivalence over $B$. Suppose there are spectral operations in families, defined as morphisms of parametrised spectra, including $\Delta_{\operatorname{fib}}^E$, $\Delta_{\operatorname{fib}}^{B\times M}$, $\Xi_{{{r}}}^B$, and $\Xi_{{{l}}}^B$. Parametrised loop coproduct obstruction conjecture. An analogue of the corresponding loop coproduct formula holds:

$$\Delta_{\operatorname{fib}}^{B\times M} \circ f_! - f\wedge f \circ \Delta_{\operatorname{fib}}^E = \Xi_{{{r}}}^B - \Xi_{{{l}}}^B.$$

This conjecture extends the obstruction formula from a single manifold to smooth fiber bundles and parametrised spectra. The source gives no evidence that it has been proved or disproved.