Do I need to upgrade to Big Sur to back up my iphone on my IMac?

In Catalina, the functions that iTunes once did for managing iDevices was moved to the Finder. Look under "Locations" in the Finder window sidebar for your phone's icon.

See: How to back up your iPhone, iPad, and iPod touch - Apple Support

you can sync with older macOS versions, it would be troublesome otherwise as not all mac computers support big sur.