We are interested in spatio-temporal dynamics of cavity solitons (CSs) in a transverse section of a broad area vertical cavity surface emitting laser (VCSEL) with saturable absorbtion subjected to time-delayed optical feedback. In the absence of delayed feedback, a single branch of localized solutions appears in the parameter space. However, in the presence of the delayed feedback, multistability of CS solutions emerges; The branches of CSs fill the surface of the "solution tube" in the parameter space, which is filled densely with increasing delay time. Further, our study reveals that the multistability of stationary solutions is caused by a delayed-induced phase bifurcation of CSs. Furthermore, it was shown that stability properties of CSs strongly depend on the delayed feedback parameters. In particular, the thresholds of the drift and phase bifurcations as well as corresponding bifurcation diagrams are obtained by a combination of analytical and numerical continuation methods. It turns out that both thresholds tend to zero in the limit of large delay times. In addition, we demonstrate that the presence of the delayed optical feedback can induce Andronov-Hopf bifurcation and a period doubling route to chaos. Moreover, a coupling between this bifurcation scenario with aforementioned delay-induced multistability leads to a complex spatio-temporal behavior of the system in question. The results of analytical bifurcation analysis are in agreement with those obtained by direct numerical integration of the model equation.