Slicing a mesh with planes

I need to slice up a mesh using planes just as is demonstrated in this video:

These instructions do not work for me because, I suspect, the Blender version used to make this video is prior to 2.8, as is shown by Its upload date. My Blender version is 2.90.1. How is this done in Blender 2.9?

I know of the Knife, and Bisect tools. These do not meet the need which is to use existing mesh planes to do the cutting.

Mostly the same way. Planes have to be in the same mesh object. Select them, and do a Face -> Intersect (Knife).

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At 0:40, how did the OP get the separated parts to arrange themselves like that?

Into the stair configuration? Shear tool.

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