Does tilt-shift photography involve moving the lens on a straight line, taking several pictures in succession, and then connecting them together?

No.

Aren’t all lenses deformed? Tilt-shift lenses take advantage of the deformation of the edges of the lens.

The principle is that the outermost lens can be moved. Move the edge of the outermost lens to the center of the image. Due to deformation, the things captured by the camera will be larger on one side and smaller on the other. At this time, the lens can make the top of the building appear larger, and the building will appear to be as wide as the top and bottom.

It was still a single photo.

By the way, tilt-shift lenses are not for daily use. Because they are all manual lenses, they cannot focus automatically.