Semi-inclusive measurements of hadron-jet acoplanarity are utilized to search for jet quenching effects in the 0--10\% most central Pb--Pb collisions at $\sqrt{s_{\text{NN}}} = 5.02~\text{TeV}$ and the high-multiplicity pp collisions at $\sqrt{s} = 13~\text{TeV}$. In the Pb--Pb system, where quark--gluon plasma formation is established, a narrowing and suppression of the acoplanarity is observed relative to the PYTHIA-simulated pp reference. In contrast, the acoplanarity distributions that were measured in the high-multiplicity pp events exhibit a marked broadening and suppression with respect to the analogous distributions obtained from the minimum bias events. The observed features are, however, qualitatively reproduced by the PYTHIA 8 Monte Carlo event generator, which does not incorporate jet quenching. The PYTHIA simulations reveal that the observed suppression and broadening are the consequence of a bias induced by the ALICE high-multiplicity trigger, which increases the probability to observe a high-$p_{\rm{T}}$ recoil jet in the acceptance of the forward trigger detectors and which biases toward multi-jet final states.