We present an analysis of ground-based and JWST observations of SN 2022pul, a peculiar "03fg-like" (or "super-Chandrasekhar") Type Ia supernova (SN Ia), in the nebular phase at 338 days postexplosion. Our combined spectrum continuously covers 0.4–14 μm and includes the first mid-infrared spectrum of a 03fg-like SN Ia. Compared to normal SN Ia 2021aefx, SN 2022pul exhibits a lower mean ionization state, asymmetric emission-line profiles, stronger emission from the intermediate-mass elements (IMEs) argon and calcium, weaker emission from iron-group elements (IGEs), and the first unambiguous detection of neon in a SN Ia. A strong, broad, centrally peaked [Ne ii] line at 12.81 μm was previously predicted as a hallmark of "violent merger" SN Ia models, where dynamical interaction between two sub-M_Ch white dwarfs (WDs) causes disruption of the lower-mass WD and detonation of the other. The violent merger scenario was already a leading hypothesis for 03fg-like SNe Ia; in SN 2022pul it can explain the large-scale ejecta asymmetries seen between the IMEs and IGEs and the central location of narrow oxygen and broad neon. We modify extant models to add clumping of the ejecta to reproduce the optical iron emission better, and add mass in the innermost region (<2000 km s⁻¹) to account for the observed narrow [O i] λλ6300, 6364 emission. A violent WD–WD merger explains many of the observations of SN 2022pul, and our results favor this model interpretation for the subclass of 03fg-like SNe Ia.