Dynamical binary interactions such as common envelope (CE) evolution or stellar mergers are a critical phase in the formation of a wide variety of binary phenomena, ranging from blue stragglers to type I supernovae (of all flavours, a, b and c), $γ$-ray bursts to bipolar planetary nebulae, Thorne-Zytkow objects to X-ray binaries. In 2040s, the urgency of resolving long-standing questions regarding the physics behind the dynamical interaction stages and the absolute and relative frequencies of binary evolutionary pathways will only increase owing to rapidly expanding population statistics of gravitational wave events. Here, we argue that multi-wavelength observations (spectroscopy and photometry), linear spectropolarimetry, and interferometry of a large number of Luminous Red Novae, a particular class of transients associated with dynamical binary interactions, will provide unprecedented details about the underlying interaction physics. A breakthrough will be achieved by a tenfold or larger increase in identifications of transient-type events from interacting binaries and their follow-up with instrumentation that provides at least 10 times better angular resolution, 100 times better spectral resolution, and $\sim$100 times higher sensitivity than 2030s facilities.
