The $\varphi^4$ model is a generalization of the Ising model to a system with unbounded spins that are confined by a quartic potential. A natural random cluster representation for the model arises by considering the sign field, which is distributed as an Ising model in a random environment. I will talk about a proof of local uniqueness of the macroscopic cluster throughout the supercritical phase of this percolation model. This serves as a crucial step towards establishing fine properties of the supercritical phase of the spin model via renormalization arguments. To illustrate this, I will discuss a proof of surface order large deviations for the empirical magnetization. Based on joint work with Christoforos Panagiotis, Romain Panis, and Franco Severo.