You are asking for a discussion midway through to restart. Cool.
Let me explain physics 101. A processor takes in electrical energy. It outputs some work, and heat. Good with the 101 now?
TDP is thermally dissipated power.
The electrical energy pulled from the wall is not TDP. It's electrical Watts. Because your processor doesn't just output heat, TDP<electrical draw.
This is how your CPU has an electrical draw, an output of thermal energy in Watts, and an efficiency for conversion from Watts (electrical) to Watts (thermal), and where input energy in electrical Watts is immensely dependent upon package temperature.
So, you pull 251 Watts at the wall (more than that, but 251 Watts for the processor package). That electrical energy is converted into heat, or thermally dissipated power, or TDP. This is how you get a package TDP of 125 Watts.
Now...that 125 is split by everything on the package. That's the CPU cores, the iGPU, and anything else. Intel provides data...that I linked to...which says just the iGPU has an output of 15 Watts thermally... that is easy to guess on electrical input because 125/251 = about 50%. This means if the iGPU is as efficient as the entire package, 15 Watts TDP = 30 Watts input electrical energy.