  We present JWST near- and mid-infrared spectroscopic observations of the
nearby normal Type Ia supernova SN 2021aefx in the nebular phase at $+255$ days
past maximum light. Our Near Infrared Spectrograph (NIRSpec) and Mid Infrared
Instrument (MIRI) observations, combined with ground-based optical data from
the South African Large Telescope (SALT), constitute the first complete optical
$+$ NIR $+$ MIR nebular SN Ia spectrum covering 0.3$-$14 $\mu$m. This spectrum
unveils the previously unobserved 2.5$-$5 $\mu$m region, revealing strong
nebular iron and stable nickel emission, indicative of high-density burning
that can constrain the progenitor mass. The data show a significant improvement
in sensitivity and resolution compared to previous Spitzer MIR data. We
identify numerous NIR and MIR nebular emission lines from iron-group elements
and as well as lines from the intermediate-mass element argon. The argon lines
extend to higher velocities than the iron-group elements, suggesting stratified
ejecta that are a hallmark of delayed-detonation or double-detonation SN Ia
models. We present fits to simple geometric line profiles to features beyond
1.2 $\mu$m and find that most lines are consistent with Gaussian or spherical
emission distributions, while the [Ar III] 8.99 $\mu$m line has a distinctively
flat-topped profile indicating a thick spherical shell of emission. Using our
line profile fits, we investigate the emissivity structure of SN 2021aefx and
measure kinematic properties. Continued observations of SN 2021aefx and other
SNe Ia with JWST will be transformative to the study of SN Ia composition,
ionization structure, density, and temperature, and will provide important
constraints on SN Ia progenitor and explosion models.
