  Next-generation detectors are expected to be sensitive to postmerger signals
from binary neutron star coalescences and thus to directly probe the remnant
dynamics. We investigate the scientific potential of postmerger detections with
the Einstein Telescope using full Bayesian analyses with the state-of-the-art
waveform model ${\tt NRPMw}$. We find that: (i) Postmerger signals with
signal-to-noise ratio (SNR) ${\sim}7$ can be confidently detected with a Bayes'
factor of $\log{\cal B}\simeq 5$ ($\rm e$-folded) and the posterior
distributions report informative measurements already at SNR ${\sim}6$ for some
noise realizations. (ii) The postmerger peak frequency $f_2$ can be confidently
identified at SNR $7$ with errors of $O(1~{\rm kHz})$, that decrease below
$O(100~{\rm Hz})$ for SNR 10. (iii) The remnant's time of collapse to black
hole can be constrained to $O(20~{\rm ms})$ at SNR 10. However, the inference
can be biased by noise fluctuationsif the latter exceed the signal's amplitude
before collapse. (iv) Violations of the EOS-insentive relations for $f_2$ can
be detected at SNR $\gtrsim 8$ if the frequency shifts are $\gtrsim 500~{\rm
Hz}$; they can be smoking guns for EOS softening effects at extreme densities.
However, the $f_2$ measurement can be significantly biased by subdominant
frequency components for short-lived remnants. In these cases, an EOS softening
might be better inferred from the remnant's earlier collapse.
