I'm new to blender, but looked at several videos and tutorials and tried to do it in 2.90.0.
Starting from a simple cube, created an array in 3D (3 arrays in X, Y and Z), fixed distance, leaving some space between them.
Entered Edit mode (array selected), here something was already strange, tried to see everything selected, was not possible until I´ve activated the Object Data Properties selector in the array modifier.
Then hit P and selected By Loose Parts, but nothing happens. Just keeps where it is.
When the Object Data Properties selector in the array modifier is NOT selected, then all the array does not select in Edit Mode.
After trying again and again, starting over, new file, etc. I´ve download version 2.83 LTS and made the same thing, and it worked. Tried 2.90.1 and this version also did not work.
Did something change in a way which is not documented and I´m missing something?