Why should equilibrium imply steady state? For example, there is a process whose rate increases with time and this process can be exactly balanced by an inverse process whose rate also increases with time.Is this not a case of non-steady state equilibrium condition?
The question is nonsense. Electrons are completely fungible — there is no way to distinguish one electron from another.
There's no meaningful way to talk about one set of electrons flowing in one direction across an interface and a different set flowing in the other direction — all you can talk about is the net flow, which as far as I can tell, is always zero in your scenario.
So yes, in that sense, the system is in equilibrium with respect to charge.
But if the temperature is rising and electron velocities are generally increasing, then it is not in thermal equilibrium.
To me, the semiconductor seems to be in thermal equilibrium but not in steady state which is contrary to the above statement in quotes. Please tell what is the thing I'm missing
You constructed an physically impossible example. If something is impossible, it can have any property you imagine. But it doesn't change the fact that it's wrong to derive any contradictions based on that.