Answer

Have a good week.
I didn’t understand the comment. Of course the equation describes the wavefunction, but the dynamics of the wavefunction depend on the potential and not on force. There is no concept of force in quantum theory. Dependence on potential is teleological rather than causal (a description in terms of force is causal). Moreover, the equation itself is a result of minimizing the Hamiltonian or the Lagrangian.
Ordinary wave equations, like an electromagnetic wave, describe a field (which is essentially force per unit charge), and therefore what I wrote is not relevant to them. There it really is a causal description, except that there is Fermat’s principle, which is an equivalent description. But in quantum theory there is only a teleological description of the dynamics and not a causal one.
The heat equation is not relevant here at all, because there is no relation there between cause and effect. It is a description of diffusion that depends on diffusion coefficients and not on any external cause (the heat equation is a diffusion equation). In wave equations there is a causal relation, because they describe the relation between the field and its sources (charges and currents). That is a relation of cause and effect.
As for the side of the equation on which the potential appears, that doesn’t seem relevant to our discussion. The potential multiplies the field, and therefore it appears with the Laplacian on the right-hand side. On the left-hand side there is the derivative with respect to time. On the contrary, such a structure means that the value of the wavefunction at the next moment depends on its value at the current moment and on the potential (and not on force). That is exactly a teleological description of its dynamics.