How to find the local sideways velocity of an object?

I’m referring to what this gentleman says in the video about creating a vehicle controller. The link below is time stamped

I have no idea how to find the sideways velocity he’s referring to. I’ve heard to use Vector3.Dot and a few other explanations, but I can’t find code on exactly how to do it Unity. I really need help getting it written out, and it’s been holding back some real progression of my vehicle controller.
I could really use the assist on this, I don’t really know what else to do.

Did you know how to do it?