It depends on what you define as illusion and what you define as reality. First I will have to define two concepts, stress and strain, in engineering terms. Stress is the application of a force per unit area, like psi. It is stress that compresses gases, but the same principle applies to solids - they just stay in more or less the same shape. Strain is a deformation of an object. If I have a 100 cm bar and I pull on it so hard it lengthens to 101 cm, it is under 1% strain. It doesn’t matter if the bar is rubber, steel, wood, or titanium - the force is different, but if it’s stretched 1%, that’s 1% strain. The stress (force) required to stretch it is different, though.
If Albert measured everything in the spaceship, assuming its engines were shut down, as it zips through space at 0.9c, he would find that there wasn’t anything distorted inside it. There would not be any extra strains from Lorenz contraction or anything of the sort measured inside the space ship. There is no difference to an observer on the spaceship whether it is traveling at 0.9c or at rest with respect to an outside observer.
On the other hand, to you, as an observer who is not moving with the spaceship, it will appear to be compressed. You can measure the deformation, perhaps by taking a picture of it and measuring the picture. You could even measure the strains from the Lorenz contraction, but only if your device for measuring strain did not move with the spaceship. Strain is defined as a change the shape of an object, so the strain would be real in your frame of reference. It would not be real to a strain gauge mounted on the spaceship, though.
Confused? It gets worse. Normally, the rule is that strain on a material is produced by applying a stress. But in the case of Lorenz contraction, the strain is not produced by any applied stress at all. There is no force changing the length of the spaceship. What is happening is that while the speed of light is a constant, all other measurements - length, time, and even mass - must change to accommodate the constant speed of light. This happens automatically, without applying any forces.
It’s hard to explain what is happening, but it is not an optical illusion. It isn’t that the material is squeezed to contract it as much as the length that the material occupies is contracted. I know this is not making any sense. It is late and relativity doesn’t even make sense to me when I am wide awake.