The potential mistake is the reference electrode's role. While the reference electrode does establish a stable potential, it is not primarily for voltage measurement in a supercapacitor. Its main role is to provide a stable reference point for the electrochemical processes occurring in the supercapacitor. Voltage measurement is typically done using external instrumentation, not the reference electrode itself.

Counter electrode acts as anode, Your supercapacitor material acts as cathode (Working electrode), Reference electrode maintains the constant potential of the cell.

Reference electrode [RE], as by its name provide a stable reference potential, so we can measure the potential difference between RE and Working electrode [WE]. Commonly used ones are Ag/AgCl, Hg/HgCl.

Counter electrode [CE] is used to collect the electrons or charge, so we can measure current between CE and WE.

That's why we use a highly conducting material like Platinum wire.