I could compare it to this question about whether the Devil's Sight invocation allows one to see into Hunger of Hadar, but that question has an easy answer, due to the 'blinded' condition it affects the person inside with. However, the spell Mordenkainen's Private Sanctum does not give the 'blinded' effect- it merely states that, in one of its properties:
The barrier of the warded area appears dark and foggy, preventing vision (including darkvision) through it.