We present a new high-precision parametric strong lensing total mass reconstruction of the Euclid Early Release Observations (ERO) galaxy cluster Abell 2390 at redshift z = 0.231. We include in this analysis 35 multiple images from 13 background sources, of which 25 are spectroscopically confirmed thanks to observations from the Multi Unit Spectroscopic Explorer (MUSE), spanning a redshift range from z = 0.535 to z = 4.877. After fully re-analysing the MUSE spectroscopy, we combined it with archival spectroscopic catalogues, thus allowing us to select 65 secure cluster members. We further complemented this sample with 114 photometric member galaxies, identified within the Euclid VIS and NISP imaging down to magnitude HE = 23. We also measured the stellar velocity dispersions for 22 cluster members in order to calibrate the Faber─Jackson relation and hence the scaling relations for the sub-halo mass components. We tested and compared 11 total mass parametrisations of the galaxy cluster with increasing complexity. To do so, we employed the new parametric strong lensing modelling code Gravity.jl. Our best-fit total mass parametrisation is characterised by a single large-scale halo, 179 sub-halo components, and an external shear term. The reference model yields a mean scatter between the model-predicted and observed positions of the multiple images of 0.″32. We were able to quantify the systematics arising from our modelling choices by taking advantage of all the different explored total mass parametrisations. When comparing our results with those from other lensing studies, we noticed an overall agreement in the reconstructed cluster total mass profile in the outermost strong lensing regime. The discrepancy in the innermost region of the cluster (a few kiloparsecs from the brightest cluster galaxy, where few or no strong lensing features are observed) could possibly be ascribed to the different data and modelling choices.