Recently, the transition metal dichalcogenide (TMD) system 2M-WS₂ has been identified as a Dirac semimetal exhibiting both superconductivity with the highest T_c ~ 8.5 K among all the TMD materials and topological surface states. Here we report on muon spin rotation (μSR) and density functional theory studies of microscopic SC properties and the electronic structure in 2M-WS₂ at ambient and under hydrostatic pressures (p_max = 1.9 GPa). The SC order parameter in 2M-WS₂ is determined to have single-gap s-wave symmetry. We further show a strong negative pressure effect on T_c and on the SC gap Δ. This may be partly caused by the pressure induced reduction of the size of the electron pocket around the Γ-point. We also find that the superfluid density n_s is weakly affected by pressure. The absence of a strong pressure effect on n_s and the absence of a correlation between n_s and T_c in 2M-WS₂, in contrast to the other SC TMDs T_d-MoTe₂ and 2H-NbSe₂, is explained in terms of its location in the optimal (ambient pressure) and above the optimal (under pressure) superconducting regions of the phase diagram and its large distance to the other possible competing or cooperating orders.