Impact of the PSR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">J</mml:mi><mml:mn>0740</mml:mn><mml:mo>+</mml:mo><mml:mn>6620</mml:mn></mml:mrow></mml:math> radius constraint on the properties of high-density matter

X-ray pulse profile modeling of PSR $\mathrm{J}0740+6620$, 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 $(1,2)\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$. 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 $0.7{5}_{\ensuremath{-}0.24}^{+0.25}{c}^{2}$ at ${3.60}_{\ensuremath{-}1.89}^{+2.25}$ times nuclear saturation density at 90% credibility. Since all but the gravitational-wave observations prefer a relatively stiff EoS, PSR $\mathrm{J}0740+6620$'s central density is only ${3.57}_{\ensuremath{-}1.3}^{+1.3}$ times nuclear saturation, limiting the density range probed by observations of cold, nonrotating neutron stars in $\ensuremath{\beta}$-equilibrium.