How can I tell whether color fringing in a smartphone camera is caused by the lens, sensor, or processing?

Chromatic Aberration

Chromatic aberration is a common fault of lenses.

Lateral or Transverse Chromatic Aberration: This is the most common type chromatic aberration. The image formed by the lens differs slightly in size according to the colour of the light. This type of CA is most noticeable in the corners of the image. It is generally not visible in the centre of the image but increases in prominence as the distance from the centre increases.

A dark object against a light background may have a coloured fringe of one colour on the side nearest the centre and a different colour on the side furthest from the centre (e.g. red fringe on one side and green fringe on the other). The effect is much the same at all apertures. It cannot be eliminated by stopping down the aperture.

Lateral chromatic aberration can be largely corrected in software. Modern mirrorless cameras usually do this correction automatically.

Axial or Longitudinal Chromatic Aberration: In this case, the focal length of the lens varies slightly with the colour of the light. It is usually most noticeable when the image is slightly out of focus. It is most apparent for very large aperture lenses and the effect is reduced as the lens is stopped down. Axial chromatic aberration can occur anywhere in the image. The distance from the centre has only a minor effect on its appearance.

Axial chromatic aberration may appear as a purple fringe that completely surrounds a dark object against a light background, often most obvious when the object is slightly out of focus.

Axial chromatic aberration cannot be automatically corrected by software (except possibly by AI techniques). It is often most troublesome in fast lenses of longer focal lengths.

Other Causes of Colour Fringing

Sometimes colour fringing is not due to the lens or the sensor, but to the way in which the image has been processed in software. Sharpening techniques often generate haloes around objects and sometimes these can show as colour fringes. Sharpening is very commonly included in image processing techniques that do not explicitly mention sharpening.

In the image included in the question above, there is a spurious pink colour to background of some of the foliage of the large tree. I have occasionally seen a very similar effect in some of my own photographs after processing. The pink colour was an artefact of the processing and was not present in the original image (with minimal processing). Unfortunately, I did not find a way to prevent the pink colour that did not change the image in other undesirable ways.