... It is really essential to understand that axis-counting is no good as a way to determine effectiveness of an IS system.
con we agree that in practice camera shake can and will occur "in any direction, sideways and rotational - in all three axes of our three-dimensional world (x, y, z) and even in any combination therof?
Yes, number of axes stabilized does not tell us anything about an IS system's effectiveness (how well it stabilizes ... 0, 1,2,3,4,+ stops - and under what conditions?). But offering stabilization in more/all directions is essential to build a dramatically better IS system than one working "in 2 directions (x,y - angular) only.
And as for in-lens IS "being specialized for each lens" this really is a marketing joke. Of course it has to be "specialized" and "built to order" for each lens, because of the differences in optical design. After all in-lens IS introduces an additional, moveable lens element/group in the light-path, which would otherwise not necessarily be needed to yield the desired imaging capabilities.
At the sensor level however, shake is shake. It has direction/s, frequency and amplitude. Amplitude will be larger, the narrower the FOV of the mounted lens, that's all. For teh system to work well, it does not have to be tailored to each lens. It just has to be effective in quickly moving the sensor exactly in the right direction/s by the required amount of travel. Irrespectively of whether a lens with 10mm lens or 800mm focal length is mounted, and what optical lyout is used in that lens.
The best in-sensor IS systems today are every bit as effective as in-lens IS ... at a fraction pof the cost. Since it is needed only once per body, not once in every single lens. The only inherent advantage of in-lens IS systems is the ability to stabilize the viewfinder image in a DSLR. In mirrorless cameras with EVF, this is not needed, since the viewfinder image comes directly from the sensor and will automatically be stabilized. No matter what lens, as long as the amplitude of the camera shake is within working limits of the IS system. :-)