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.
And please make sure you communicate an expectation: that you can’t be the only one doing all the small chores.
I am in control of my own life. All small chores will cower in fear before me. No one can carry this burden but me. (Because it only takes a few minutes)