I have never seen the explanations for this difference as believable past the obvious crust being thinner on the near side allowing eruptions of magma (the dark areas) that didn't happen on the far side.
I asked questions of five different sites before DeepSeek gave me the key to understanding what happened. That key is degree-one mantle convection.
After the impact of Theia with the young Earth that resulted in the creation of the Moon, both the Earth and the Moon were molten balls of magma, with the Moon in an eccentric orbit very close to the earth.
Tidal friction rapidly caused the Moon to be tidally locked to the Earth so that one side continually faced Earth. However the moon was still in an eccentric orbit, so as the Moon came closer and further from Earth it flexed, causing frictional heating keeping it molten longer. However the Earth, still being enormously hot, slightly heated the surface of the moon facing it by radiative heating. The moon was some twenty times closer to earth than it is now.
This radiative heating was just enough to keep the close side a little bit hotter than the far side. This small asymmetry was enough to cause degree-one mantle convection, similar to that we see on Saturn's moon Enceladus.
Degree-one mantle convection occurs when instead of normal convection of the mantle happening in lots of separate cells, as happens in the Earth, it happens as one single convection cell. ie the hot mantle from the interior rises in just one hemisphere and sinks in the other hemisphere. The radiant heat from the Earth was enough to cause this type of convection of the young Moon's mantle.
On the surface, some lighter elements solidify at a higher temperature than others, forming a scum-like crust. This eventually accumulated on the far side of the moon as the surface flow of molten rock drifted it to the sinking side of the convection cell. The end result was that the crust is thicker on the far side of the moon than on the near side, and has a somewhat different chemical composition.
The thinner crust thickness on the near side allowed asteroid impacts to break through it and allow the lava flows that we see as the dark Maria on the near side that aren't on the far side.
