  Recent JWST observations of the Type Ia supernova (SN Ia) 2021aefx in the
nebular phase have paved the way for late-time studies covering the full
optical to mid-infrared (MIR) wavelength range, and with it the hope to better
constrain SN Ia explosion mechanisms. We investigate whether public SN Ia
models covering a broad range of progenitor scenarios and explosion mechanisms
can reproduce the full optical-MIR spectrum of SN 2021aefx at $\sim$270 days
post explosion. We performed 1D steady-state non-LTE simulations with the
radiative-transfer code CMFGEN, and compared the predicted spectra to SN
2021aefx. The models can explain the main features of SN 2021aefx over the full
wavelength range. However, no single model, or mechanism, emerges as a
preferred match. We discuss possible causes for the mismatch of the models,
including ejecta asymmetries and ionisation effects. Our new calculations of
the collisional strengths for Ni III have a major impact on the two prominent
lines at 7.35 and 11.00 $\mu$m, and highlight the need for more accurate
collisional data for forbidden transitions. Using updated atomic data, we
identify a strong feature due to [Ca IV] 3.21 $\mu$m, attributed to [Ni I] in
previous studies. We also provide a tentative identification of a forbidden
line due to [Ne II] 12.81 $\mu$m, whose peaked profile indicates the presence
of neon all the way to the innermost region of the ejecta, as predicted for
instance in violent merger models. Contrary to previous claims, we show that
the [Ar III] 8.99 $\mu$m line can be broader in sub-$M_\mathrm{Ch}$ models
compared to near-$M_\mathrm{Ch}$ models. Our models suggest that key physical
ingredients are missing from either the explosion models, or the
radiative-transfer post-processing, or both. Nonetheless, they also show the
potential of the near- and MIR to uncover new spectroscopic diagnostics of SN
Ia explosion mechanisms.
