Stellar metallicity gradients (∇[Z/H]) provide a fossil record of the assembly history of galaxies. We present an analysis of ∇[Z/H] for 90 nearby low-mass galaxies using Very Large Array (VLT)/MUSE integral field unit (IFU) spectroscopy, spanning stellar masses from 106.5 to 1010M⊙(median ∼108.5M⊙) and significantly extending the mass coverage of existing IFU surveys into the classical dwarf regime. Our primary finding is a robust negative correlation between ∇[Z/H] and light-weighted stellar age (∣r∣ ≳ 0.7) measured out to ∼2× effective radius: older dwarf galaxies have steeper (more negative) gradients. This holds regardless of stellar mass, structural compactness, or large-scale environment (group/field) and is strongest in the intermediate-mass regime ( 8.2≲logM⋆/M⊙≲9.0 ). The slope of the age─∇[Z/H] relation is close to that in the FIRE-2 simulations, indicating that stellar radial migration driven by feedback-induced potential fluctuations may be fundamental in dwarf evolution. But this apparent consistency is likely coincidental given the simulations' overly efficient feedback and chemical mixing. On the other hand, the H I deficiency parameter, an indicator of past environmental stripping, shows a moderate yet highly significant correlation with ∇[Z/H], second only to stellar age in strength: galaxies with higher H I deficiency tend to have more negative gradients, strongly indicating that environment-driven outside-in quenching and the ensuing gradual truncation of metal enrichment reshape the stellar metallicity distribution. Our analysis suggests that the chemical evolution of dwarf galaxies likely arises from a synergy of feedback-driven dynamical heating and external environmental processing, though only the latter has robust observational support.