Your measurements of length are certainly altered but space itself is not altered. For example, if you travel from here to Alpha Centauri at a relativistic velocity, the length between Earth and Alpha Centauri, to YOU, appears to shorten. However, the space between Alpha Centauri and Earth is not actually changing, as anyone who measures it from either Earth or Alpha Centauri, or any other point in the universe can confirm. Only YOUR measurement is changing.
I’m not disputing that when you do the math that time and the spatial dimensions are interchangeable. However, these are just mathematical conventions. In reality, time and space are clearly different things, even if we can conceptually represent them as interchangeable axes in a coordinate system for our own convenience. Einstein’s entire focus in relativity was solving the problem of SIMULTANEITY in moving systems, which is a temporal problem, not a spatial one. His use of Minkowski space to unify the mathematics of space and time to solve the problem works, but it has the unfortunate side effect of creating this confusion that time and the spatial dimensions are interchangeable IN REALITY, when they are really only interchangeable in this limited mathematical framework.
“the space between Alpha Centauri and Earth is not actually changing, as anyone who measures it from either Earth or Alpha Centauri, or any other point in the universe can confirm. Only YOUR measurement is changing.”
This entirely misses a central point of special relativity: there is no such thing as THE distance between A and B. Any measurement in an inertial frame of reference is as valid as any other.