Ultracapacitor initial voltage drop during discharging
Using only the ESR from the datasheet (ideal wires...):





Current is practically zero before discharging and jumps to 10A, hence the drop. Initial linear discharge is expected due to constant current.

The larger drop you see is certainly due to wires, switches etc.

To be more specific, let's consider 3 steps:


charging: capacitor practically reached its max. voltage, current through ESR, from the voltage source, is mainly due to leakage (max 5.2 mA in the datasheet)
both switches opened: current through ESR is zero but capacitor is self discharging due to leakage (could be modeled by a 520 Ohm in parallel with the cap)
discharging: current through ESR follows the load current