The state of being very wet and soft, like when you leave your sandwich in your lunchbox all day and it gets wet and gross.
Sogginesses are usually not good because things are not supposed to be wet and gross.
Examples:
The sogginesses of the sandwich made it uneatable.
I don't like the sogginesses of wet socks.
The sogginesses of the ground made it hard to walk.
The sogginesses of the cereal made it like eating a sponge.
The sogginesses of the rain made everything outside very wet.
The sogginesses of the bread made it fall apart in my hands.