The half-filled 𝑡2𝑔 shell of the configuration usually, in 𝐿𝑆 coupling, hosts a 𝑆=3/2 ground state with quenched orbital moment. This state is not Jahn-Teller active. Sufficiently large spin-orbit coupling 𝜁 has been predicted to change this picture by mixing in orbital moment, giving rise to a sizable Jahn-Teller distortion. In 5𝑑3K2ReCl6 we study the electronic excitations using resonant inelastic x-ray scattering and optical spectroscopy. We observe on-site intra-𝑡2𝑔 excitations below 2 eV and corresponding overtones with two intra-𝑡2𝑔 excitations on adjacent sites, the Mott gap at 2.7 eV, 𝑡2𝑔-to-𝑒𝑔 excitations above 3 eV, and charge-transfer excitations at still higher energy. The intra-𝑡2𝑔 excitation energies are a sensitive measure of 𝜁 and Hund's coupling 𝐽H. The sizable value of 𝜁≈0.29eV places K2ReCl6 into the intermediate coupling regime, but 𝜁/𝐽H≈0.6 is not sufficiently large to drive a pronounced Jahn-Teller effect. We discuss the ground state wave function in a Kanamori picture and find that the 𝑆=3/2 multiplet still carries about 97% of the weight. However, the finite admixture of orbital moment allows for subtle effects. We discuss small temperature-induced changes of the optical data and find evidence for a lowering of the ground state by about 3 meV below the structural phase transitions.