  Light-matter interactions provide an ideal testground for interplay of
critical phenomena, topological transitions, quantum metrology and
non-Hermitian physics. We consider two fundamental non-Hermitian
Jaynes-Cummings models which possess real energy spectra in parity-time (PT)
symmetry and anti-PT symmetry. We show that the quantum Fisher information is
critical around the transitions at the exceptional points and exhibits a super
universality with respect to different parameters, all energy levels, both
models, symmetric phases and symmetry-broken phases. The transitions are found
to be both symmetry-breaking Landau-class transitions (LCTs) and
symmetry-protected topological-class of transitions (TCTs), thus realizing a
simultaneous occurrence of critical LCTs and TCTs which are conventionally
incompatible due to contrary symmetry requirements.
