Does a space being a timespace/spacetime by default grant the space being universal in size?

No, being a timespace/spacetime does not necessarily mean that the space is universal in size. The concept of spacetime refers to the unified understanding of space and time as a single entity, as described by the theory of relativity. However, the size of the universe is a separate concept that is determined by the expansion of the universe and the limits of our observable universe. The size of the universe is constantly changing and expanding, so it is not necessarily universal in size.