Nobody really has any idea what "dark energy" is. But there is a principle known as Occam's razor. It can be expressed in various ways, for example "When an observation can be explained in many ways, the one with fewest assumptions should be used."
To explain the properties of dark energy as being due to changing pressure of hyperspace, requires the assumption that "hyperspace" exists, that it has a property that pressurizes the universe, that this "pressure" is changing, and that affects the rate of expansion of the universe.
There are other hypothesis: a cosmological constant, or a as yet undiscovered force field. None have much observational evidence, but have the benefit of requiring fewer assumptions.
As Rob mentioned what you describe is similar to "brane cosmology", in which the universe is embedded in a higher dimensional space. These could influence our space, by controlling the scale of a cosmological constant, making it small, but non-zero. As with much of string theory, the experimenters are well behind the theorists.
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