ZTF-SEDm Type Ia supernova sample for Twins Embedding spectrophotometric standardisation

This paper has two aims: the first one is to build a large homogeneous spectrophotometric Type Ia supernova (SN Ia) sample, using 3069 spectra from the second Zwicky Transient Facility data release (ZTF DR2). Using this sample we reproduce, as the second objective of the paper, the Twins Embedding (TE) spectrophotometric standardisation method, which led to an exceptionally low value of 0.073 mag for the intrinsic scatter. We improve the flux-calibration accuracy of the SEDm SN Ia spectral sample using the ZTF photometric data, which are calibrated at the percent level. We then apply the three steps of the TE parameterisation to a subset of 783 ZTF SN spectra near maximum light, and analyse the resulting standardisation methods. The precision of the phase correction model, which is the first step of the TE, is estimated at 0.01 mag in g band, using ZTF data. Despite the challenge posed by the ZTF spectrum extraction pipeline, we apply a first standardisation in color based on the second step of the TE, the Read Between The Lines (RBTL). When considering the scatter due to the redshift error and the flux calibration error, we estimate a 0.129 mag Hubble residual scatter for this ZTF sample as an upper limit. As expected from the low spectral quality, the final TE standardisation based on three non-linear parameters did not improve the overall dispersion. We release 1897 flux calibrated spectra of 1607 SNe Ia with an estimated photometric accuracy of 0.07 mag. We further demonstrate the ability to apply a spectrophotometric standardisation with limited quality spectra. The RBTL standardisation is more efficient than that of SALT with one less parameter, and the resulting host steps are consistent with zero, making it less prone to astrophysical bias. For future spectroscopic surveys, a better spectral quality would enable the full TE standardisation to be computed. (Abridged)