The ALICE collaboration has measured the production of $K^{0}{S}$ and $\Xi^{\pm}$ in \textit{pp} collisions at $\sqrt{s}=13$TeV in the direction of the leading charged particle and in the direction transverse to it. The $\Xi^{\pm}$ yield normalized to the $K^{0}{S}$ yield is found to increase with the charged particle multiplicity for both the transverse-to-leading and the toward-leading (jet-like) regions. Although the enhancement in the transverse-to-leading region, which is sensitive to the underlying event, can be understood as due to medium(-like) effects, the enhancement for the jet-like region is striking. The effect in the jet-like region is qualitatively reproduced by PYTHIA8 with rope hadronization and EPOS LHC. The medium(-like) effects in the leading charged particle $p_{T}$ spectrum using different Monte Carlo models (AMPT, EPOS4 with and without hydrodynamics and PYTHIA8 with the color ropes mechanism) are studied. A medium(-like)-free $p_{T}$ leading threshold for angular correlation studies involving high $p_{T}$ hadrons is reported, where the leading particle $p_{T}$ spectrum is unaffected by medium(-like) effects. Since the measurements reported by ALICE were performed considering a significantly lower $p_{T}$ leading threshold, the apparent strangeness enhancement in the jet-like region can be explained in terms of a bias due to the misidentification of the leading particle.