  We study lepton flavour universality violation in SM boson decays in
low-scale seesaw models of neutrino mass generation, also addressing other
electroweak precision observables. We compute the electroweak next-to-leading
order corrections, which turn out to be important - notably in the case of the
invisible decay width of the $Z$ boson, for which the corrections can be as
large as the current experimental uncertainty. As a well-motivated illustrative
study case, we choose a realisation of the Inverse Seesaw mechanism, and
discuss the complementary role of lepton flavour conserving, lepton flavour
violating and precision observables, both in constraining and in probing such
models of neutrino mass generation. Our findings suggest that invisible $Z$
decays are especially important, potentially at the origin of the most
stringent constraints for certain regimes of the Inverse Seesaw (while
complying with charge lepton flavour violation and other electroweak precision
tests). We also discuss the probing power of the considered observables in view
of the expected improvement in experimental precision at FCC-ee.
