We present recent tests of lepton universality as crucial probes of the Standard Model in semileptonic $B$-meson decays at Belle II. All presented analyses use a data sample collected at the $\Upsilon(4S)$ resonance by the Belle II experiment corresponding to an integrated luminosity of $189\,\mathrm{fb}^{-1}$. We report three analyses that probe light-lepton universality: The first measurement of a complete set of five angular asymmetries using $\bar{B}^0 \to D^{*+} \ell^- \bar{\nu}_\ell$ decays, followed by a measurement of the forward-backward asymmetry in untagged $\bar{B}^0 \to D^{*+} \ell^- \bar{\nu}_\ell$ decays, and finally, measurements of the branching-fraction ratios $R(D^{*+}_{e/\mu}) = \mathcal{B}(\bar{B}^0 \to D^{*+} e^- \bar{\nu}_e) / \mathcal{B}(\bar{B}^0 \to D^{*+} \mu^- \bar{\nu}_\mu)$, using the same untagged data set, along with the first measurement of the inclusive light-lepton ratio $R(X_{e/\mu}) = \mathcal{B}(\bar{B} \to X e^- \bar{\nu}_e)/\mathcal{B}(\bar{B} \to X \mu^- \bar{\nu}_\mu)$. Furthermore, we present two tests of heavy-to-light lepton universality. In the first test, we report the measurement of the branching-fraction ratio $R(D^{*}_{\tau/\ell})$ using hadronic tagging. In the second test, we present the first measurement of the inclusive ratio $R(X_{\tau/\ell})$. All presented results are consistent with their corresponding Standard Model predictions and, where applicable, with the experimental world averages.