LDO peak-to-peak voltage 280mV
As the spikes are present on both 12V input and 3.3V output, so they come from the 12V switching mode power supply that is ungrounded.

The switching spikes couple capacitively from the mains side to the isolated 12V side, and the charging currents loop via oscilloscope probe ground wire back to mains earth. The voltage bounce comes from inductance of the scope probe ground lead which is not able to handle fast currents.

So part of the issue is how the probes are connected.