Dc and ac magnetizations were measured for the 3D nanocomposite consisted of Ga-Ag dendritic grains embedded into a porous glass template with the aim to study the impact of the particular morphology on superconductivity. The temperature range of measurements was from 1.8 to 10 K. The Ga-Ag alloy composition corresponded to the eutectic point (97 at.% Ga, 3 at.% Ag). The nanocomposite behaved as a dirty type-II superconductor with strong pinning, transition temperature near 7.03 K, and enhanced upper critical field. We found a phase diagram with the positive curvature of the upper critical field line at low magnetic fields and a crossover to the negative curvature that correlated to the bend on the field dependence of the vortex potential barriers. We suggested that both the curvature crossover and bend on the field dependence of potential barriers evidenced a vortex structure transformation associated with destroying intergrain links. Other changes in the vortex structure appeared as steps on the dc FC curves and hysteresis between the FC magnetizations obtained upon cooling (FCC) and warming (FCW). These phenomena were not found in the earlier studies of nanocomposites with inclusions of pure Ga and Sn and might be related to the strong heterogeneity of the confined Ga-Ag eutectic alloy.