Regarding solo air forks everything is clear. Once we bumped both chambers pressure is equal. But why for dual air forks air pressure doesn't try to get equal in both chambers? What's the point of second chamber if it has different pressure and doesn't try to equal it?
The negative air chamber provides resistance to the positive air chamber. It controls the speed air spring returns to its initial shape. The chambers are isolated so the air is unable to equalise.
The positive chamber provides resistance against compression, essentially how hard is the fork.
The third part of the suspension action is dampening, the negative air chamber controls the forks return and the damper stops if from oscillating and provides a smooth ride.
Rockshox explain dual air below quite well in suspension terms.