How do you update software that says it is up to date

Clearly if it's up to date there can be no further updates, and this is the case with your iPhone 6s.

The 6s cannot be updated beyond iOS 12.5.6 and this is why you have not seen any updates being offered for your device.

Edit to the above - my text should have read iPhone 6 Plus, not iPhone 6s.

The 6s and 6s Plus can be updated to iOS 15.7.1

iPhone 6 Plus can’t be updated to any versions above iOS 12. You can download security updates though (Although they get released every few months.)