I’ll go first. After your turn the water off in the shower but before you get out, use your hands to wipe off any standing water on your body. Maybe even give your legs a bit of a shake. This way, you won’t drip nearly as much when you get out, keeping the floor and your towel drier.
But why upside down. Just leave them filled with water in sink.
Reduce air exposure and conserve water, especially with bowls and containers that are deeper than a dish.
Utensils will get dried eventually when upside down and you’ll have to wash them within few minutes or wetting utensils would be of no use.