So, for a Dash 8-100, at 13,000 kg, disregarding drag, engine efficiency, etc, to take-off and climb to 1000m and accelerate to 150 knots (77 m/s), you will need:

- 13000 * 9.81 * 1000 = 127.5 MJ, to reach your altitude

- 0.5 * 13000 * (77)^2 = 38.5 MJ, to accelerate to your climbing speed.

Total: 127 + 38.5 = 166 MJ, or about 46.11 kWh

For a go around, re-accelerating from 1.3 * stall speed (85 knots / 44 m/s) to your climbing speed, and going to your missed approach altitude of 1000 m, you will need:

- 13000 * 9.81 * 1000 = 127.5 MJ, to reach your altitude

- 0.5 * 13000 * (77^2 - 44^2) = 26 MJ to accelerate back to your climbing speed.

Total: 127 + 26 = 153 MJ, or about 42.5 kWh

You don't do a full climb after a go-around, so the heights are not equal, and the mass is less since you've expended fuel. You also retain some kinetic energy but I assume that is closer to a negligible effect.

Also, PE = mgh is probably an not a great formula for energy cost of takeoff/go-around, as there are probably large costs it ignores (gravity loss, less efficient engine use, maybe less efficient turbines?).

For your source 2 I have no rebuttal so will have to defer to you, but would ask for an explanation.

Time to invent regenerative air brakes, like fold-out windmills.