Stellar feedback plays a significant role in modulating star formation, redistributing metals, and shaping the baryonic and dark structure of galaxies - however, the efficiency of its energy deposition to the interstellar medium is challenging to constrain observationally. Here we leverage HST and ALMA imaging of a molecular gas and dust shell (M_{ H_2} ˜ 2× 105 M_{⊙ }) in an outflow from the nuclear star-forming ring of the galaxy NGC 3351, to serve as a boundary condition for a dynamical and energetic analysis of the outflowing ionized gas seen in our MUSE TIMER survey. We use STARBURST99 models and prescriptions for feedback from simulations to demonstrate that the observed star formation energetics can reproduce the ionized and molecular gas dynamics - provided a dominant component of the momentum injection comes from direct photon pressure from young stars, on top of supernovae, photoionization heating, and stellar winds. The mechanical energy budget from these sources is comparable to low luminosity active galactic neuclei, suggesting that stellar feedback can be a relevant driver of bulk gas motions in galaxy centres - although here ≲10-3 of the ionized gas mass is escaping the galaxy. We test several scenarios for the survival/formation of the cold gas in the outflow, including in situ condensation and cooling. Interestingly, the geometry of the molecular gas shell, observed magnetic field strengths and emission line diagnostics are consistent with a scenario where magnetic field lines aided survival of the dusty ISM as it was initially launched (with mass-loading factor ≲1) from the ring by stellar feedback. This system's unique feedback-driven morphology can hopefully serve as a useful litmus test for feedback prescriptions in magnetohydrodynamical galaxy simulations.