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We study the abundance of satellite galaxies around 198 Milky Way- (MW) and M31-like hosts in TNG50, the final instalment in the IllustrisTNG suite of cosmological magnetohydrodynamical simulations. MW/M31-like analogues are defined as disky galaxies with stellar masses of Mstar = 10^10.5-11.2 Msun in relative isolation at z = 0. By defining satellites as galaxies with Mstar > 5*10^6 Msun within 300 kpc (3D) of their host, we find a remarkable level of diversity and host-to-host scatter across individual host galaxies. The median (16th - 84th percentiles) TNG50 MW/M31-like galaxy hosts a total of 5 (2-11) satellites with Mstar > 5*10^6 Msun, reaching up to Mstar ~ 10^8.5 Msun (10^7.4-9.4 Msun). The abundance of subhaloes with Mdyn > 5*10^7 Msun is larger by a factor of more than 10. The number of all satellites (subhaloes) ever accreted is larger by a factor of 4-5 (3-5) than those surviving to z = 0. Hosts with larger galaxy stellar mass, brighter K-band luminosity, larger total halo mass, and more recent halo assembly typically have a larger number of surviving satellites. The satellite abundances around TNG50 MW/M31-like galaxies are consistent with similar hosts from observational surveys (e.g. SAGA) and previous simulations (e.g. Latte). While the observed MW satellite system falls within the TNG50 scatter across all stellar masses considered, M31 is slightly more satellite-rich than our 1 sigma scatter, possibly due to volume and mass limitations. We find a handful of systems with both a Large and a Small Magellanic Cloud-like satellite. There is no missing satellites problem with TNG50., Accepted by MNRAS. TNG50 is publicly available at https://www.tng-project.org/