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This paper presents the first measurement of the angle between different jet axes (denoted as $\mathrm{\Delta }{R}_{\mathrm{axis}}$ ) in $\text{Pb-Pb}$ collisions. The measurement is carried out in the 0–10 % most-central events at $\sqrt{s_{NN}}=5.02$ TeV. Jets are assembled by clustering charged particles at midrapidity using the $\text{anti-}{k}_{\mathrm{T}}$ algorithm with resolution parameters $R=0.2$ and 0.4 and transverse momenta in the intervals $40<p_{\mathrm{T}}^{\mathrm{ch}\mathrm{jet}}<140\mathrm{GeV}/c$ and $80<p_{\mathrm{T}}^{\mathrm{ch}\mathrm{jet}}<140\mathrm{GeV}/c$ , respectively. Measurements at these low transverse momenta enhance the sensitivity to quark-gluon plasma (QGP) effects. A comparison to models implementing various mechanisms of jet energy loss in the QGP suggests that the observed narrowing of the $\text{Pb-Pb}$ distribution relative to $\mathit{pp}$ can be explained if quark-initiated jets are more likely to emerge from the medium than gluon-initiated jets. These new measurements disfavor intrajet $p_{\mathrm{T}}$ broadening as implemented in a simple model calculation with the Baier-Dokshitzer-Mueller-Peigne-Schiff formalism for energy loss in the QGP. The comparison of $\text{Pb-Pb}$ and $\mathit{pp}$ collisions shows sensitivity to the angular scale at which the QGP can resolve two independent splittings, favoring mechanisms that incorporate incoherent energy loss.