  The process of emission of electromagnetic radiation does not occur
instantaneously but it is "formed" over a finite time known as radiation
formation time. In the ultrarelativistic regime, the corresponding
(longitudinal) formation length is given by the formation time times the speed
of light and controls several features of radiation. Here, we elucidate the
importance of the transverse formation length (TFL) by investigating nonlinear
Compton scattering by an electron initially counterpropagating with respect to
a \emph{flying focus} laser beam. The TFL is related to the transverse size of
the radiation formation "volume" and, unlike the longitudinal formation length,
has a quantum origin. Being the TFL typically of the order of the Compton
wavelength, where any laser field can be assumed to be approximately uniform,
related quantum interference effects have been ignored. However, we show
analytically that if the focus in a flying focus beam with $n_L\gg 1$ cycles
moves at the speed of light and backwards with respect to the beam propagation
direction, the effects of the TFL undergo a large enhancement proportional to
$n_L$ and may substantially alter the differential emission probability for
feasible flying focus pulses.
