Is it inappropriate to ask department staff for syllabi previously used for courses I am to teach in upcoming year?
Actually, it is quite appropriate. You could also ask for a list of the professors who previously taught the course. You could then ask them if they are willing to share materials to help bootstrap the course.
In fact, the administrative assistant might not have easy access directly, partly due to the pandemic. But the professors would normally retain their materials.
You might also find recent course information online if each course has a website or if professors have websites with course material.