By means of extensive simulations, we investigate concentrated solutions of globular single-chain nanoparticles (SCNPs), an emergent class of synthetic soft nano-objects. By increasing the concentration, the SCNPs show flattening, and even reentrant behaviour, in the density dependence of their structural and dynamical correlations, as well as a soft caging regime and weak dynamic heterogeneity. The latter is confirmed by validation of the Stokes-Einstein relation up to concentrations far beyond the overlap density. Therefore SCNPs arise as a new class of soft colloids, exhibiting slow dynamics and actualizing in a real system structural and dynamical anomalies proposed by models of ultrasoft particles. Quantitative differences in the dynamical behaviour depend on the SCNP deformability, which can be tuned through the degree of internal cross-linking.