Far field spherical waves plane waves
Rajeev Bansal in the appendix to this article explains the $2D/\lambda$ rule:

How does one arrive at the various criteria for the far-field zone?
Basically, the criteria are guidelines to the boundaries where the
fields start to approximate the “ideal” assumed characteristics. First
of all, only the radiation ($1/r$) terms remain significant; higher
order terms fade away. Second, in the far-field zone, the angular
field distribution becomes independent of the distance [5]. Third,
only transverse field components remain, and the ratio of the electric
and magnetic field components approaches the free-space impedance, 377
ohms [6 ,7]. Finally, for a receiving antenna, the incoming wave-front
is nearly planar across the aperture. In fact, the $r = 2 D^2/\lambda$
formula corresponds to a phase error (due to the curvature of the
actual spherical wave-front) of no more than $\pm 22.5$ degrees across the
aperture, as compared with the ideal plane wave-front [6, 8].
References:

IEEE Standard Dictionary of Electrical and Electronics Terms, IEEE standard 100-1984, 1984.

C. Paul, K. Whites, and S. Nasar, Introduction to Electromagnetic Fields, 3rd ed., McGraw-Hill, 1998.

Reference Data for Radio Engineers, 6th ed., SAMS, 1981.

G. Smith, An Introduction to Classical Electromagnetic Radiation, Cambridge, 1997.