Annihilation dynamics plays a fundamental role in the baryon–antibaryon interaction (B–B‾) at low-energy and its strength and range are crucial in the assessment of possible baryonic bound states. Experimental data on annihilation cross sections are available for the p–p‾ system but not in the low relative momentum region. Data regarding the B–B‾ interaction with strange degrees of freedom are extremely scarce, hence the modeling of the annihilation contributions is mainly based on nucleon–antinucleon (N–N‾) results, when available. In this letter we present a measurement of the p–p‾, p–Λ‾⊕p‾–Λ and Λ–Λ‾ interaction using correlation functions in the relative momentum space in high-multiplicity triggered pp collisions at s=13 TeV recorded by ALICE at the LHC. In the p–p‾ system the couplings to the mesonic channels in different partial waves are extracted by adopting a coupled-channel approach with recent χEFT potentials. The inclusion of these inelastic channels provides good agreement with the data, showing a significant presence of the annihilation term down to zero momentum. Predictions obtained using the Lednický–Lyuboshits formula and scattering parameters obtained from heavy-ion collisions, hence mainly sensitive to elastic processes, are compared with the experimental p–Λ‾⊕p‾–Λ and Λ–Λ‾ correlations. The model describes the Λ–Λ‾ data and underestimates the p–Λ‾⊕p‾–Λ data in the region of momenta below 200 MeV/c. The observed deviation indicates a different contribution of annihilation channels to the two systems containing strange hadrons.