  X-ray pulse profile modeling of PSR J0740+6620, the most massive known
pulsar, with data from the NICER and XMM-Newton observatories recently led to a
measurement of its radius. We investigate this measurement's implications for
the neutron star equation of state (EoS), employing a nonparametric EoS model
based on Gaussian processes and combining information from other x-ray, radio
and gravitational-wave observations of neutron stars. Our analysis mildly
disfavors EoSs that support a disconnected hybrid star branch in the
mass-radius relation, a proxy for strong phase transitions, with a Bayes factor
of $6.9$. For such EoSs, the transition mass from the hadronic to the hybrid
branch is constrained to lie outside ($1,2$) $M_{\odot}$. We also find that the
conformal sound-speed bound is violated inside neutron star cores, which
implies that the core matter is strongly interacting. The squared sound speed
reaches a maximum of $0.75^{+0.25}_{-0.24}\, c^2$ at $3.60^{+2.25}_{-1.89}$
times nuclear saturation density at 90% credibility. Since all but the
gravitational-wave observations prefer a relatively stiff EoS, PSR J0740+6620's
central density is only $3.57^{+1.3}_{-1.3}$ times nuclear saturation, limiting
the density range probed by observations of cold, nonrotating neutron stars in
$\beta$-equilibrium.
