The Syracuse application asks whether you’ve had a paid job and, if so, what it taught you. Syracuse is really asking two things: whether you’ve had to earn things in your life instead of having them given to you, and (relatedly) whether you have a strong work ethic.
Consider every application to be asking these questions.
Work ethic should emanate from every part of an application: grades, extracurriculars, recommendations. Your whole application should show (and this is a life principle, really) that whatever privileges you’ve had, you’ve also worked very hard (i.e., that if you’ve been lucky enough to go to a great school, you’ve worked like crazy to learn and excel there). That seems pretty obvious, but it’s important to remember.
And regarding the paid job thing: colleges are justifiably impressed by someone who works for money. Not only on applications, but also in life, plan to be able to say, “Yes, I’ve worked.” Working in a store or restaurant is good. Babysitting, odd jobs, and camp counseling are also fine. Realistically, it’s been really difficult for teenagers to get any jobs in the past two years, so your answer to the job question could also be: “No. Because I didn’t have to work/couldn’t find a job, I was able to spend my time volunteering/interning/taking care of my siblings. Here’s what I did/learned.”