How can I update my iPad Mini 2 if showing it is up to date with iOS 9.3.6

If its showing 9.3.6 is up to date, its not an iPad Mini 2. Its an iPad Mini 1 Cellular, as that iOS version was only available for that model of iPad Mini. See here: Identify your iPad model - Apple Support

You cannot update that iPad Mini beyond that iOS version sorry. Apple security updates - Apple Support

Hello,

If your iPad will not update past 9 then you have an iPad mini (1st generation). This iPad model does not support any system version newer than 9. You cannot update your iPad any further. If you need to use software that requires a newer system software version then you will need to purchase a newer iPad model.

You can’t update it any further. You have reached the end of the line for software support on that device. You need to upgrade to a newer device if you want to run a newer iOS versions.