Compact stars in Einstein-scalar-Gauss-Bonnet gravity: Regular and divergent scalar field configurations

We investigate static, spherically symmetric solutions in Einstein-scalar-Gauss-Bonnet gravity nonminimally coupled to a massless real scalar field, both in vacuum and in the presence of fermionic matter. Focusing on a specific quadratic scalar--Gauss--Bonnet coupling, we identify two distinct classes of compact objects: one with a regular scalar field at the origin---connected to general relativity in an appropriate limit---and another one with a divergent scalar field at the origin but a regular geometry. We analyze both purely scalar and matter-supported (hybrid) configurations, showing that the former can describe a broad class of compact objects, while the latter can reproduce neutron starlike masses even when modeled with a simple polytropic equation of state. Furthermore, we highlight distinctive phenomenological signatures, including the ability of these stars to exceed known compactness limits and their potential to act as gravitational wave superemitters. We also examined the motion of test particles nonminimally coupled to the scalar field and showed the existence of stable circular orbits within the Schwarzschild's ISCO and static configurations at finite radii for particles with zero angular momentum.