For a traditional tire that is inflated enough to be in the proper operating range, with smooth-ish tread (ie, not aggressive bar or lug tires), the ground pressure will always be within a couple % of the inflation pressure (many times it will match almost exactly). So if you want to minimize the ground pressure, look for the mower that specs the lowest PSI inflation pressure for the tires. It's that simple. Even if you don't do an exact calculation and just want to find the best mower for soft ground, look for the one with the lowest PSI inflation specs for the tires.
We can prove this with a fairly routine physics derivation or very basic experiment, but it's become enough of an engineering rule of thumb that I think you can just run with it. This rule of thumb breaks with run-flat tires or tires with sidewalls stiff enough to support weight at zero inflation pressure. It only works on tires that require air pressure to support weight. It also breaks with tires that have aggressive tread. A mower turf tire is on the opposite extreme, and fits the model pretty well.