Three dimensions would seem to be a mapping device, like longitude, latitude and altitude. As such, an abstraction of the subject, not the basis for it.

Given that in a frame moving at the speed of light, both measures of distance and duration shrink to zero, what if we go the other direction, to the frame with the longest ruler and fastest clock? Wouldn't it be closest to the equilibrium of the vacuum? The unmoving void of absolute zero?

While curved space might be an interesting and useful concept, all measures of space on the broadest scales show it is over-all flat. The apparent outward curvature between galaxies is balanced by the inward curvature into them. "Omega =1."

Which would mean it is infinite.

So the apparent conceptual parameters of space are infinity and equilibrium. Like the number line, from zero to infinity.