  We study the properties of hybrid stars containing a color superconducting
quark matter phase in their cores, which is described by the chirally symmetric
formulation of the confining relativistic density functional approach. It is
shown that depending on the dimensionless vector and diquark couplings of quark
matter, the characteristics of the deconfinement phase transition are varied,
allowing us to study the relation between those characteristics and mass-radius
relations of hybrid stars. Moreover, we show that the quark matter equation of
state (EoS) can be nicely fitted by the Alford-Braby-Paris-Reddy model that
gives a simple functional dependence between the most important parameters of
the EoS and microscopic parameters of the initial Lagrangian. Based on it, we
analyze the special points of the mass-radius diagram in which several
mass-radius curves intersect. Using the found empirical relation between the
mass of the special point, the maximum mass of the mass-radius curve, and the
onset mass of quark deconfinement, we constrain the range of values of the
vector and diquark couplings of the quark matter model. With this constraint,
we construct a family of mass-radius curves, which allow us to describe the
black widow pulsar PSR J0952-0607 with a mass of $2.35\pm 0.17~\rm M_\odot$ as
a hybrid star with a color superconducting quark matter core.
