what follows is not exactly your case (you consider specific conditions as acid solution, etc.) but I think it that this example can give an idea of the definition and characteristics of the double layer that forms on an electrode.
When a metal (M) is placed in a solution of its own salt (Mn+) one of the two processes are possible:
(i) Metal atoms go into solution in the form of ions.
M → Mn+ + ne- (Oxidation)
(ii) Metal ions from solution may deposit on the metal.
Mn+ + ne- → M (Reduction)
In the first case metal atoms get converted into metal ions, which enters into solution leaving behind the electrons in the metal itself and making it negatively charged.
Example: When Zn electrode is dipped in ZnSO4 solution, Zn goes into solution as Zn2+ ions.
In the second case metal ions present in the solution deposit over the metal and gains electrons and making it positively charged.
Example : When Cu electrode is dipped in CuSO4 solution, Cu2+ ions from solution deposit on the metal.
Thus a layer of positive or negative ions formed all around the metal. This layer is called Helmholtz electrical double layer, which results a potential difference between the metal ions and the solution.
At equilibrium, the potential difference becomes a constant value which is known as the electrode potential of the metal. Thus the tendency of the electrode to lose electrons is called Oxidation potential and tendency of an electrode to gain electrons is called Reduction potential.
Single electrode potential (E): It is the tendency of a metallic electrode to lose or gain electrons when it is in contact with a solution of its own salt.
Standard electrode potential (Eo): It is the tendency of a metallic electrode to lose or gain electrons when it is in contact with a solution of its own salt of 1M concentration at 25oC.
For more details, please see at the source: https://www.svce.ac.in/departments/chemistry/CITM/CY%206251/Engg.%20Chem.%20II%20word/Unit%20II%20-%20Electrochemistry.pdf
and at the interesting notes of Dr. Basherer: https://mail.uotechnology.edu.iq/dep-chem-eng/LECTURE%202014-2015/4Y/crrosion_Basheer_2.pdf
and of Dr. Rajalakshmi: http://www.rajalakshmi.org/downloads/CY19142.pdf
When a metal is in contact with electrolyte, there may be the formation of electrical double layer. An electrical double layer structure looks like a capacitor, i.e. seperation of two different conducting phases by any insulator. In this case, the charged (mostly negative) working electrodes is seperated from charged (mostly positive) ions in the bulk electrolyte. These are seperated by a insulator called dielectric. But the seperation is very minimal usually few angstroms.
Usually, double layer consists of different phases such as Inner Helmholz plane, outer Helmholz plane and diffusion phase. The values of such capacitance can be find using EIS or CV testings.
IN GENERAL, double layer capacitance values are inversely proportional to the corrosion resistance.