Op Amp Input Offset Voltage vs Common Mode Voltage
This is a common characteristic of rail-to-rail input op-amps. There are really two front ends and there is a transition between them at some common-mode voltage. R-R output is irrelevant.

If you care about Vos to that extent, you can choose another type of op-amp. Maybe a chopper type, but they have other subtle (and not so subtle) imperfections.