Dark energy is most directly related to the theory of the Big Bang in that it causes the expansion of the universe to accelerate.
According to current cosmological models, after the Big Bang, the universe began to expand. Initially, this expansion was slowing down due to gravitational attraction among matter. However, observations in the late 1990s revealed that not only is the universe expanding, but that this expansion is accelerating, leading to the hypothesis of dark energy. Dark energy is thought to make up about 68% of the total energy content of the universe, and it acts in opposition to gravity, driving the acceleration of the universe's expansion.
The other statements you provided, such as dark energy causing the spinning of galaxies or seeding the formation of galaxies and star clusters, are not accurate in the context of what we currently understand about dark energy and its role in cosmic evolution.
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