This one explains the 'contracted out' issue:
https://forcespensionsociety.org/202...econciliation/
The calculation was done when you started to draw your state pension and Equiniti would have been sent a notification of what you Contracted Out Deduction was. They have no way to check whether what DWP tell them is right - a bit like the tax code, they are told what it is and have to apply it.