  We present detailed spectral and temporal characteristics of the persistent
X-ray emission of SGR J1935+2154 based on our XMM-Newton and Chandra
observations taken in the aftermath of its April 2020 burst storm, during which
hundreds of energetic X-ray bursts were emitted, including one associated with
an extraordinary fast radio burst. We clearly detect the pulsed X-ray emission
in the XMM-Newton data. An average spin-down rate of 1.6$\times$10$^{-11}$ s
s$^{-1}$ is obtained using our spin period measurement combined with three
earlier values reported from the same active episode. Our investigations of the
XMM-Newton and Chandra spectra with a variety of phenomenological and
physically-motivated models, concluded that the magnetic field topology of SGR
J1935+2154 is most likely highly non-dipolar. The spectral models indicate that
surface field strengths in somewhat localized regions substantially exceed the
polar value of 4.4$\times$10$^{14}$ G inferred from a spin-down torque
associated with a rotating magnetic dipole.
