Pls see last picture of post No.17
Yes I see large current loops with 10 nH/cm added to your schematic for every jumper and BB ground strip and mutual coupling everywhere resulting in a flyback pulse around 1 cycle at 20 MHz. This is where 2 pF diff. Probes are needed to remove measurement error from inductive ground and probe capacitance.
These spikes are well beyond the servo BW of the regulator yet V=I*ESR+LdI/dt results in spikes . Try to estimate reasons for signals, using what you know.
If you do not have diff probes, use a series cap+50Rs to SMA 50 ohm coax to 50 ohm terminated DSO using same small <2cm loop , you can capture better results with 50% atten.
The value of a ground plane is a low impedance from low geometric ratios of gap height, H to conductor width, W for high current slew rates
for
e.g. H/W= 12 ratio on FR4 determines Zo=150 ohms or H/W=1, Zo < 70 ohms
for Height of FR4 dielectric, H[mm] and track width, W[mm]
in your case with air dielectric and a huge gap for H/L ratio, your Zo is very high > 300 ohms resulting in a mismatch >= 10 MHz.
To use a breadboard, all highspeed signals need twisted magnet wire with orthogonal wiring on inductive high-speed H fields and core to minimize coupling.