  The intrinsically superconducting Dirac semimetal 2M-WS$_{2}$ is a promising
candidate to realize proximity-induced topological superconductivity in its
protected surface states. A precise characterization of the bulk
superconducting state is essential for understanding the nature of surface
superconductivity in the system. Here, we perform a detailed experimental study
of the temperature and nonmagnetic disorder dependence of the London
penetration depth $\lambda$, the upper critical field $H_{c2}$, and the
superconducting transition temperature $T_c$ in 2M-WS$_{2}$. We observe a
power-law dependence $\lambda(T) - \lambda(0) \propto T^{3}$ at temperatures
below $0.35~T_c$, which is remarkably different from the expected exponential
attenuation of a fully gapped isotropic $s$-wave superconductor. We then probe
the effect of controlled nonmagnetic disorder induced by 2.5 MeV electron
irradiation at various doses and find a significant $T_c$ suppression rate.
Together with the observed increase of the slope $dH_{c2}/dT|_{T=T_c}$ with
irradiation, our results reveal a strongly anisotropic $s^{++}$ multiband
superconducting state that takes the same sign on different Fermi sheets. Our
results have direct consequences for the expected proximity-induced
superconductivity of the topological surface states.
