  To get distances, Type Ia Supernovae magnitudes are corrected for their
correlation with lightcurve width and colour. Here we investigate how this
standardisation is affected by the SN environment, with the aim to reduce
scatter and improve standardisation. We first study the SN Ia stretch
distribution, as well as its dependence on environment, as characterised by
local and global (g-z) colour and stellar mass. We then look at the
standardisation parameter $\alpha$, which accounts for the correlation between
residuals and stretch, along with its environment dependence and linearity. We
finally compute magnitude offsets between SNe in different astrophysical
environments after colour and stretch standardisation, aka steps. This analysis
is made possible due to the unprecedented statistics of the ZTF SN Ia DR2
volume-limited sample. The stretch distribution exhibits a bimodal behaviour,
as previously found in literature. However, we find the distribution means to
decrease with host stellar mass at a 9.0$\sigma$ significance. We demonstrate,
at the 14.3$\sigma$ level, that the stretch-magnitude relation is non-linear,
challenging the usual linear stretch-residuals relation. Fitting for a
broken-$\alpha$ model, we indeed find two different slopes between stretch
regimes ($x_1<-0.49\pm0.06$): $\alpha_{low}=0.28\pm0.01$ and
$\alpha_{high}=0.09\pm0.01$, a $\Delta_{\alpha}=-0.19\pm0.01$ difference. As
the relative proportion of SNe Ia in the high-/low-stretch modes evolves with
redshift and environment, this implies that a linear $\alpha$ also evolves with
redshift and environment. Concerning the environmental magnitude offset
$\gamma$, we find it to be greater than 0.14 mag regardless of the considered
environmental tracer used (local or global colour and stellar mass), all
measured at the $\geq 6\sigma$ level, increased to $\sim0.18\pm0.01$ mag when
accounting for the stretch-non linearity.
