  With the aim of exploring the evidence for or against phase transitions in
cold and dense baryonic matter, the inference of the sound speed and
equation-of-state for dense matter in neutron stars is extended in view of
recent new observational data. The impact of the heavy (2.35 $M_\odot$) black
widow pulsar PSR J0952-0607 and of the unusually light supernova remnant HESS
J1731-347 is inspected. In addition a detailed re-analysis is performed of the
low-density constraint based on chiral effective field theory and of the
perturbative QCD constraint at asymptotically high densities, in order to
clarify the influence of these constraints on the inference procedure. The
trace anomaly measure, $\Delta = 1/3 - P/\varepsilon$, is also computed and
discussed. A systematic Bayes factor assessment quantifies the evidence (or
non-evidence) of low averaged sound speeds $(c_s^2 \leq 0.1)$, a prerequisite
for a phase transition, within the range of densities realized in the core of
neutron stars. One of the consequences of including PSR J0952-0607 in the data
base is a further stiffening of the equation-of-state, resulting for a 2.1
solar-mass neutron star in a reduced central density of less than five times
the equilibrium density of normal nuclear matter at the 68\% level. The
evidence against small sound speeds in neutron star cores is further
strengthened. Within the inferred 68\% posterior credible bands, only a weak
first-order phase transition with a coexistence density interval $\Delta n/n
\lesssim 0.2$ would be compatible with the observed data.
