The ATLAS Collaboration has recently measured Higgs boson production and decay rates, as well as differential cross-sections, in various decay channels using up to 139 fb⁻¹ of proton-proton collision data at √s = 13 TeV recorded at the Large Hadron Collider. This paper presents multiple interpretations of these measurements. The measurements are reparameterized in terms of the impact of Standard Model effective field theory (SMEFT) operators, and constraints are reported on the corresponding Wilson coefficients. Additionally, the measurements are interpreted in UV-complete extensions of the Standard Model, such as the two-Higgs-doublet model (2HDM) near the alignment limit and the Minimal Supersymmetric Standard Model (MSSM) for various benchmark scenarios. The constraints on the 2HDM parameters (cos(β − α), tanβ) and the MSSM parameters (mA, tanβ) complement those obtained from direct searches for additional Higgs bosons. The paper is structured into several sections, covering the data samples, signal simulation, signal yield parameterization, fiducial differential cross-section measurements, and interpretations based on SMEFT and UV-complete models. The interpretations are detailed for both the SMEFT framework and the 2HDM and MSSM models, providing a comprehensive analysis of the Higgs boson properties and constraints on new physics.The ATLAS Collaboration has recently measured Higgs boson production and decay rates, as well as differential cross-sections, in various decay channels using up to 139 fb⁻¹ of proton-proton collision data at √s = 13 TeV recorded at the Large Hadron Collider. This paper presents multiple interpretations of these measurements. The measurements are reparameterized in terms of the impact of Standard Model effective field theory (SMEFT) operators, and constraints are reported on the corresponding Wilson coefficients. Additionally, the measurements are interpreted in UV-complete extensions of the Standard Model, such as the two-Higgs-doublet model (2HDM) near the alignment limit and the Minimal Supersymmetric Standard Model (MSSM) for various benchmark scenarios. The constraints on the 2HDM parameters (cos(β − α), tanβ) and the MSSM parameters (mA, tanβ) complement those obtained from direct searches for additional Higgs bosons. The paper is structured into several sections, covering the data samples, signal simulation, signal yield parameterization, fiducial differential cross-section measurements, and interpretations based on SMEFT and UV-complete models. The interpretations are detailed for both the SMEFT framework and the 2HDM and MSSM models, providing a comprehensive analysis of the Higgs boson properties and constraints on new physics.