Capacitor in presence of an external electric field
In other words, is the electric field between the plates the original external incident E field or is it the E field generated by the charges separated by the original incident E field?

Using Superposition theorem
Electric field between the plates is due to
1.Electric field of electromagnetic wave 2.induce charges of 1st plate 3.induce charges of 2nd plate .
Net electric field between the plates $$=\vec(E)+\vec(E_1)+\vec(E_2)+\vec(E_3)+\vec(E_4)$$
But if plates are very very close to each other then we can assume that they will behave as parllel sheet of infinite length and we get net electric field between plates is $$\vec(E)$$  because  between  plates $$\vec(E_1)+\vec(E_2)+\vec(E_3)+\vec(E_4)=0$$
and final distribution will look like -

And from uniqueness theorem  this distribution is unique(but function of time ) for a given wave and charges on conductor (=0).
But what if plates are not very close to each other ?
Then we cannot assume as parllel sheet of infinite length and hence a distorted field will be obtained in between of plates and for that we have to solve Laplace equations with suitable boundary conditions which is too complicated
Note-$$\vec(E),\vec(E_1),\vec(E_2),\vec(E_3),\vec(E_4) $$ are electric field due to electromagnetic wave, due to induce charges on 1st plate (2 surface) and due to induce charges on 2nd plates (2surface) respectively.