Recent measurements of the inclusive $\mathrm{t\overline{t}}$ production cross section, $\sigma_\mathrm{t\overline{t}}$, and the ratio of $\mathrm{t\overline{t}}$ to Z boson production, $R_{\mathrm{t\overline{t}}/\mathrm{Z}}$, are presented by the CMS and ATLAS collaborations using data collected from proton-proton collisions at the new LHC operating energy of $\sqrt{s}=13.6$ TeV. These are among the first results of the ongoing LHC Run 3 data-taking period, which began in 2022, and provide a first opportunity to measure changes in key physics observables following the increase in energy. Both experiments used new techniques relative to previous measurements to obtain precise results efficiently, the methods of which are outlined and compared.