  We extend the FONLL general-mass variable-flavour-number scheme to the case
of longitudinally polarised DIS structure functions, accounting for
perturbative corrections up to $\mathcal{O}(\alpha_s^2)$. We quantify the
impact of charm quark mass and higher-order perturbative corrections on
projected measurements of inclusive and charm-tagged longitudinal asymmetries
at the Electron-Ion Collider (EIC) and at the Electron-ion collider in China
(EicC). We demonstrate how the inclusion of these corrections is essential to
compute predictions with an accuracy that matches the projected precision of
the measurements. The computation is made publicly available through the
open-source EKO and YADISM programs
