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.