I made some more measurement on the input of the power supply (on the filter capacitors) and I found that the fluctuations are also present there.
Vout=26.6V, Ilim=3A, Iload=2.88A.
1. No load, with the GND clip connected to the GND of 7812: 285,287.jpg
2. With load, with the GND clip connected to the GND of 7812: 292,293.jpg
3. No load, with the GND clip connected to the GND of filter capacitors: 294,296.jpg
4. With load, with the GND clip connected to the GND of filter capacitors: 298, 299.jpg
Please have a look at the screenshots and tell me what you think.