You can find a lot of others with this problem, especially some Nikon primes. Apparently, also zooms like yours. It is reflection from the glass in front of the sensor that reflects back to the lens rear element.

The colour and power of the spot depends on camera/lens combination, but often it is reddish (pink, magenta, whatever you want to call it) because some NIR-cut filters reflects a lot of it back.

(Filters are specified with transmission , absorption and reflection wavelengths. They do not cut 100%, and to cut a wavelength you can absorb it or reflect it. To absorb it absorbs some heat, so sometimes they choose to reflect instead. )

These reflections (both the NIR and visible reflections) can be reflected back into the sensor, When the surface normal points towards the sensor (which it does in the center!) thus increasing the power relative to the true signal. The true signal is pretty dim at F22, which is why you can see it at F22. Some users have reported red spots from F16, thus recommending to use minimum F11.

The reason is it not perfectly centered is because the true lens center and sensor center are not aligned perfectly, which is why camera calibration seeks to estimate the true center, and such a calibration can only be trusted for one focus distance and in case of zoom lens, one f-setting.

Hope this explanation wasnt too convoluted.