back up to family

You can share a storage plan. When you do that, you continue to use your own Apple ID for iCloud and continue to backup in the same way as if you weren't using a shared plan. When you share a plan, only the billing and the amount of storage change. See the information in Share iCloud+ with your family - Apple Support

For backup instructions, see: How to back up your iPhone, iPad, and iPod touch with iCloud - Apple Support

See the "Switch from your iCloud+ plan to your family plan" section in the support document you posted from. Link-> Share iCloud+ with your family - Switch - Apple Support