The paper explores the emergence of nonreciprocal superradiant phase transitions and multicriticality in a cavity quantum electrodynamics (QED) system. The system consists of a two-level atom interacting with two counter-propagating modes of a whispering-gallery-mode (WGM) microcavity, which is rotating at a certain angular velocity and directionally squeezed by a unidirectional parametric pumping $\chi^{(2)}$ nonlinearity. This setup enables nonreciprocal first- and second-order superradiant phase transitions, which do not require ultrastrong atom-field couplings and can be controlled by the external pump field. The authors identify two types of multicritical points in the phase diagram, both exhibiting controllable nonreciprocity. These findings open new avenues for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering integrated nonreciprocal quantum devices. The work combines theories of phase transitions, multicriticality, and nonreciprocal physics, providing a foundation for further theoretical and experimental explorations in quantum technology.The paper explores the emergence of nonreciprocal superradiant phase transitions and multicriticality in a cavity quantum electrodynamics (QED) system. The system consists of a two-level atom interacting with two counter-propagating modes of a whispering-gallery-mode (WGM) microcavity, which is rotating at a certain angular velocity and directionally squeezed by a unidirectional parametric pumping $\chi^{(2)}$ nonlinearity. This setup enables nonreciprocal first- and second-order superradiant phase transitions, which do not require ultrastrong atom-field couplings and can be controlled by the external pump field. The authors identify two types of multicritical points in the phase diagram, both exhibiting controllable nonreciprocity. These findings open new avenues for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering integrated nonreciprocal quantum devices. The work combines theories of phase transitions, multicriticality, and nonreciprocal physics, providing a foundation for further theoretical and experimental explorations in quantum technology.