  The photometric catalogue of galaxy clusters extracted from ESA Euclid data
is expected to be very competitive for cosmological studies. Using
state-of-the-art hydrodynamical simulations, we present systematic analyses
simulating the expected weak lensing profiles from clusters in a variety of
dynamic states and at wide range of redshifts. In order to derive cluster
masses, we use a model consistent with the implementation within the Euclid
Consortium of the dedicated processing function and find that, when jointly
modelling mass and the concentration parameter of the Navarro-Frenk-White halo
profile, the weak lensing masses tend to be, on average, biased low by 5-10%
with respect to the true mass, up to z=0.5. Using a fixed value for the
concentration $c_{200} = 3$, the mass bias is diminished below 5%, up to z=0.7,
along with its relative uncertainty. Simulating the weak lensing signal by
projecting along the directions of the axes of the moment of inertia tensor
ellipsoid, we find that orientation matters: when clusters are oriented along
the major axis, the lensing signal is boosted, and the recovered weak lensing
mass is correspondingly overestimated. Typically, the weak lensing mass bias of
individual clusters is modulated by the weak lensing signal-to-noise ratio,
related to the redshift evolution of the number of galaxies used for weak
lensing measurements: the negative mass bias tends to be larger toward higher
redshifts. However, when we use a fixed value of the concentration parameter,
the redshift evolution trend is reduced. These results provide a solid basis
for the weak-lensing mass calibration required by the cosmological application
of future cluster surveys from Euclid and Rubin.
