## 2 Methods  
First, we consider a two-level system for our numerical model, for which the Hamiltonian \(\mathrm{H_{2 vl}}\) is described as a matrix with two states at energy \(\mathrm{E_{g}}=0\) eV and \(\mathrm{E_{e}}=60.15\) eV, for the ground and the excited state, respectively, which are coupled in dipole approximation by the dipole matrix element \(\mathrm{d_{ge}}=\mathrm{d_{eg}}=-0.035\) a.u. (a.u. = atomic units; which are used throughout this work unless stated otherwise). The parameters are chosen to match the relative energy separation and dipole coupling strength between the 1s\({}^{2}\) ground state and the 2s2p doubly excited state in helium [21]. Hereby at first, we explicitly neglect the configuration interaction with the ionization continuum of the 2s2p doubly excited state, but still take its finite autoionization lifetime into account by means of the excited-state decay parameter \(\mathrm{hT_{e}}=37\) meV. Going one step further, we consider a second model, where we account for the configuration interaction between the excited state and the one-electron ionization continuum by extending our first model to a three-level system with Hamiltonian \(\mathrm{H_{3 vl}}\), which additionally includes an energetically broad quasi-continuum state that serves as a short-lived ionization-loss channel for the system. The parameters of this quasi-continuum state are set to energy \(\mathrm{E_{c}}=32.654\) eV, decay width \(\mathrm{hT_{c}}=39.728\) eV, dipole matrix element \(\mathrm{d_{gc}}=\mathrm{d_{cg}}=0.675298\) a.u. for its dipole coupling to the ground state and configuration interaction \(\mathrm{V_{CI}}=0.0373209\) a.u. for the inter-channel coupling between the quasi-continuum state and the 2s2p state. In this three-level system, the excited-state parameters are slightly altered to the excited-state energy \(\mathrm{E_{e}}=60.122\) eV and to the dipole matrix element \(\mathrm{d_{ge}}=-0.0493158\) a.u. for dipole coupling to the ground state, while the previously introduced direct decay of the excited state can be omitted (\(\mathrm{hT_{e}}=0\) eV), since its autoionization is now explicitly taken into account through \(\mathrm{V_{CI}}\). The numerical parameters of this three-level system have been chosen such that the weak-field transient absorption profile of the 1s\({}^{2}\)-2s2p transition agrees with the reported literature values [21], most importantly now also including its asymmetric line shape. See also Figure 1b for a simplified energy-level scheme of the system. The XUV laser pulse is treated as a classical electric field \(\mathrm{E(t)}\) with a Gaussian envelope of duration \(\mathrm{T_{FWHM}}=3\) fs (intensity full width at half maximum). To summarize, the Hamiltonian matrices \(\mathrm{H_{3 vl}}\) and \(\mathrm{H_{2 vl}}\) for the three- and two-level system, respectively, are given by:  
\[\mathrm{H_{3 vl}}=\left( \begin{array}{ccc}\mathrm{E_{g}}&\mathrm{d_{ge}\;E(t) }&\mathrm{d_{gc}\;E(t)}\\ \mathrm{d_{ge}\;E(t)}&\mathrm{E_{e}}&\mathrm{V_{CI}}\\ \mathrm{d_{gc}\;E(t)}&\mathrm{V_{CI}}&\mathrm{E_{c}+i\;\Gamma_{c}/2}\end{array}  \right),\;\mathrm{and}\;\mathrm{H_{2 vl}}=\left( \begin{array}{ccc}\mathrm{E_{ g}}&\mathrm{d_{ge}\;E(t)}\\ \mathrm{d_{ge}\;E(t)}&\mathrm{E_{e}+i\;\Gamma_{e}/2}\end{array} \right), \tag{1}\]  
with the numerical parameters as defined above. The time-dependent Schrodinger equation is solved on a discrete time grid (time steps \(\Delta\mathrm{t}=0.1\) a.u. = \(2.42\) as) through numerical diagonalization of the Hamiltonian at each time step. The state vector of the system, \(\left|\Psi(t)\right\rangle^{\left(2\mathrm{lvl}\right)}=\left[c_{g}(t),c_{e}(t) \right]^{T}\) or \(\left|\Psi(t)\right\rangle^{\left(3\mathrm{lvl}\right)}=\left[c_{g}(t),c_{e}(t),c_{c}(t)\right]^{T}\), is expressed through the complex-valued coefficients \(c_{i}\) (i = g, e, c). For the initial state, only the ground state is populated (\(c_{g}(t=0)=1\)).