  We analyze an open many-body system that is strongly coupled at its
boundaries to interacting quantum baths. We show that the two-body interactions
inside the baths induce emergent phenomena in the spin transport. The system
and baths are modeled as independent spin chains resulting in a global
non-homogeneous XXZ model. The evolution of the system-bath state is simulated
using matrix-product-states methods. We present two phase transitions induced
by bath interactions. For weak bath interactions we observe ballistic and
insulating phases. However, for strong bath interactions a diffusive phase
emerges with a distinct power-law decay of the time-dependent spin current
$Q\propto t^{-\alpha}$. Furthermore, we investigate long-lasting current
oscillations arising from the non-Markovian dynamics in the homogeneous case,
and find a sharp change in their frequency scaling coinciding with the triple
point of the phase diagram.
