The LHC collides protons at 13.6 TeV, producing a massive dataset to study rare processes and search for new physics. The production of a Higgs boson in association with a single top quark (tH) in the multi-lepton final state (2 same-sign leptons or 3 charged leptons) is particularly promising, but challenging to analyze due to undetected neutrinos and fake leptons. The tH process is especially interesting because its small Standard Model cross section originates from a subtle destructive interference between diagrams including the Higgs coupling to the W boson and the Higgs coupling to the top quark. This makes tH uniquely sensitive: even small deviations from the Standard Model can strongly enhance its production rate. The measurement of the tH cross section is delicate because the ttH and ttW processes have similar topologies and much larger cross sections, requiring a simultaneous extraction to obtain a reliable result and properly account for correlations between signals. ATLAS observed a moderate excess of tH using the Run 2 dataset (2.8 s), making the analysis of Run 3 data including these correlations crucial. The thesis will first exploit AI algorithms based on Transformer architectures to reconstruct event kinematics and extract observables sensitive to the CP nature of the Higgs-top coupling. In a second phase, a global approach will be adopted to analyze simultaneously the ttW, ttZ, ttH, tH, and 4-top processes, searching for anomalous couplings, including those violating CP symmetry, within the framework of the Standard Model Effective Field Theory (SMEFT). This study will provide the first complete measurement of tH in the multi-lepton channel with Run 3 data and will pave the way for a global analysis of rare processes and anomalous couplings at the LHC in this channel.