Not yet reviewed by Pith; the record is open.

The second data release of Type Ia supernovae (SNe Ia) observed by the Zwicky Transient Facility has provided a homogeneous sample of 3628 SNe Ia with photometric and spectral information. This unprecedented sample size enables us to better explore our currently tentative understanding of the dependence of host environment on SN Ia properties. In this paper, we make use of two-dimensional image decomposition to model the host galaxies of SNe Ia. We model elliptical galaxies as well as disk/spiral galaxies with or without central bulges and bars. This allows for the categorisation of SN Ia based on their morphological host environment, as well as the extraction of intrinsic galaxy properties corrected for both cosmological and atmospheric effects. We find that although this image decomposition technique leads to a significant bias towards elliptical galaxies in our final sample of galaxies, the overall results are robust. By successfully modelling 728 host galaxies, we find that the photometric properties of SNe Ia found in disks and in elliptical galaxies, correlate fundamentally differently with their host environment. We identified strong linear relations between light-curve stretch and our model-derived galaxy colour for both the elliptical (16.8$\sigma$) and disk (5.1$\sigma$) subpopulations of SNe Ia. Lower stretch SNe Ia are found in redder environments, which we identify as an age/metallicity effect. Within the subpopulation of SNe Ia found in disk containing galaxies, we find a significant linear trend (6.1$\sigma$) between light-curve stretch and model-derived local $r$-band surface brightness, which we link to the age/metallicity gradients found in disk galaxies. SN Ia colour shows little correlation with host environment as seen in the literature. We identify a possible dust effect in our model-derived surface brightness (3.3$\sigma$), for SNe Ia in disk galaxies.