  In quantum optics, photonic Schr\"odinger cats are superpositions of two
coherent states with opposite phases and with a significant number of photons.
Recently, these states have been observed in the transient dynamics of
driven-dissipative resonators subject to engineered two-photon processes. Here
we present an exact analytical solution of the steady-state density matrix for
this class of systems, including one-photon losses, which are considered
detrimental for the achievement of cat states. We demonstrate that the unique
steady state is a statistical mixture of two cat-like states with opposite
parity, in spite of significant one-photon losses. The transient dynamics to
the steady state depends dramatically on the initial state and can pass through
a metastable regime lasting orders of magnitudes longer than the photon
lifetime. By considering individual quantum trajectories in photon-counting
configuration, we find that the system intermittently jumps between two cats.
Finally, we propose and study a feedback protocol based on this behaviour to
generate a pure cat-like steady state.
