That used to be a thing. The Crapper Toilet company used to have a sprung toilet seat. It was of mixed success. The rubber stops on the bottom of the seat were made of natural rubber. As the rubber oxidized it would get sticky. This led to the seat sticking to the bowl for a moment. Then spring up and hitting you in the ass as you stood up. It gained the name the crapper clapper.
Mostly though do you really want a seat sliding up your ass as you stand up?
Can you touch the toilet seat when you are standing? I can't. It seem one would have to hold ot down stand half way. Make a 180° turn, then let go as you stand up all the way. All with you pants around your ankles.
I am going to stick with manual toilet seats. I wouldn't stop you it you want to make a spring loaded one.