I asked a question with the same meaning on Quora, but it seems no one got it, so I'm asking it here with a very different wording. I'm actually not sure if this would belong here or on the Astronomy stack exchange, as though it deals with the Earth, it is an extremely pure question with almost nothing to do with its atmosphere or complicated innards. Real-world topographic and atmospheric moisture conditions that may affect the results are to be ignored.
For all latitudes outside the tropics, as I'm sure we know, the summer solstice is the date where the sun culminates the highest in the sky, having the highest solar angle and insolation. This angle is 90° at the tropical circles. Closer to the equator, this 90° angle is experienced in 2 Lāhainā noons moving further from the solstice the lower the latitude is until reaching the equinoxes at the equator.
However, at all locations except the equator, the summer solstice is the longest day of the year and the winter solstice the shortest. Hence, down to a certain latitude within the tropics the summer solstice should still experience the most total solar energy, as the effect of the longer day would be stronger than that of the lower solar angle. As you get closer to the equator, the day length gets more consistent and the angle at the solstice becomes still further from that at the subsolar point, until eventually the solstice no longer receives the most total solar energy and two "humps" emerge.
So, what is that latitude?
Note: This answer can depend on if the eccentricity of the Earth's orbit is taken into account, in which case the values for the Northern and Southern hemispheres will be different. Answers may choose to take this into account or not (ideally I'd like both).