Especially for an introvert/generally shy person, what would be the best ways to show leadership to selective/ivy schools? I’m thinking create/lead decent sized clubs with familiar people (so you don’t get nervous) or just forming small groups to do social impact projects. One of which I’m doing (social impact projects w/ friends), but I am open to any other effective ideas.
That’s a great idea! If you start a club about something you are passionate with your friends it will make it immensely easier be in charge of it. In addition it will help you make friends with people passionate about the same things as you 
If its Ivy schools you want to impress you may want to form something more tangible than a just forming small groups for projects, instead maybe form a club focused on doing these social projects. But whatever you decide to do, remember, don’t do something just for the sake of impressing a school, do it because you truly want to do it.
I do interviews and leadership i have seen:
-Student involved in ethnic community center for years and then is asked to teach little kids
-Actual officer in a club
-Watched his little brother after school and encouraged parents to sign up brother for sports team and took him to practice
-Within a club, organized an activity for that club
-Lead a community service activity
-Lead singer of a band - sings, chooses set list, organizes transportation for other members
-Summer Camp counselor
-Boy Scout Eagle Award/Girl Scout Gold Award
-EMT Cadet
-Boys State/Girls State