Would you use a female urination device to be able to pee standing up in a public restroom?

No way. Cover toilet seat with a liner or paper, or lift toilet seat and straddle avoiding skin contact or do same after covering with toilet paper. You would need to wash, rinse, dry and carry around such a device. There is no point.
One could do this. I am not aware of a commercially available device but I would not be surprised that such a device is out in the market - over 10 years ago a colleague and i designed and patented a female urinary collection device for this purpose. It was primary used by female astronauts in the US and European space programs.