Hi, I think, its always a dynamic (!) equilibrium and only by convention you can assume that it is in a steady state (e.g.

First please be aware that a stable open circuit potential does not necessarily define an equilibrium state. It is only an equilibrium if the paired reduction and oxidation that define the open circuit are the forward and reverse of the same electron transfer reaction (ignoring complex ECE mechanisms that may define an equilibrium state through an intermediate reaction). In corrosion, in particular, a stable open circuit defines a steady state potential, not an equilibrium.

Second, note that while no measurement device is perfect (input impedance is one aspect, though potentiostats have that value at more like 10^15 Ohms) unless your system is very sensitive to any current (e.g. barrier coatings, some "stainless" passivating alloys...typically high nickel varieties), it is far more likely that a long time to reach a stable OCP or not reaching one at all is really just the nature of the [material]-[electrolyte] interface. Some systems don't reach steady state (or at least not for a very long time).

Third, and back to your first question: what is physically happening varies with the system. Passive film formation is one possibility, water infiltration/uptake into a film could be another. In general, balancing all the Nernst equations between the electrode material, electrolyte activity (basically any/all electroactive species) is what leads to a stable OCP.