How does blade solidity ratio relate to thrust/power/torque of a propeller?
Each propeller blade is a wing in itself, and like a wing carries the weight of the plane, the propeller blade carries its fraction of the total thrust of the propeller. The more blades, the lower the fraction of each blade.

Low disc loadings are associated with two- or three-bladed propellers. Those can be found on GA aircraft and older, slow designs like pre-WW II aircraft. With turboprops and near-transsonic designs, more blades are needed to distribute the aerodynamic loads and to reduce the lift coefficient especially at the tips.

There is no strict formula, but in general a higher disk loading is associated with a higher solidity ratio.