Illustrator gives the size only as apparent height and width. Illustrator doesn't care nor know that your drawing can present objects in 3D space. Illustrator knows only one plane (=the artboard).
Illustrator knows 3D only in a certain case: 3D effects can hold one object at a time in 3D space and that happens just when the effect is adjusted. Before and after it the object is a planar shape on the artboard.
Affinity D creates for you three different grids which are the rectangular grids on XY,XZ and YZ planes projected onto your artboard plane. You have no actual 3D depth, but drawing along those projected girds can create fake parallel 2D projections of 3D objects. All parallel planes are projected equally to your artboard because there's no perspective, so it's enough to have only the projected grids available on the artboard.
Actually one projected rectangular grid would be enough for drawing in isometric projection, but Affinity D gives to you all three for convenience. They all are needed if the projection is other than isometric. You see the grid of the current "working plane".
If you change the projection the already drawn parts do not adapt, they are only flat objects on your artboard.
Affinity D calculates the dimensions of the drawn objects as real 3D dimensions and shows the selection boxes as SkewedScaledRotated rectangles instead of the usual horizontal boxes. To make it happen you must have the selector tool option "Cycle Selection Boxes" =ON.
The Transform panel shows the straight on the face dimensions of the drawn object. There's also the rotation and skew angles which would transform the straight on the face rectangle to be seen on the drawing plane.
BTW. Option "Cycle Selection Boxes" is harmfully switched OFF as soon as you change the working plane.