My mom when to Catholic school and wrote in cursive all the time although I had a very hard time reading her perfect Catholic cursive which seemed to differ in peculiar ways with my public school scribbles. I got a "D" in penmanship and had to work hard to write in cursive. Today I type.
To answer your question regarding how Gen Z signs its name - it doesn't. If they are forced to "sign" then they take their finger and squiggle it across some electronic device to create some meaningless graphic. Honestly I hope someone challenges that some day and says that's not MY signature - it's a friggin worm!