Living systems are maintained out of equilibrium by external driving forces. At stationarity, they exhibit emergent selection phenomena that break equilibrium symmetries and originate from the expansion of the accessible chemical space due to nonequilibrium conditions. Here, we use the matrix-tree theorem to derive upper and lower thermodynamic bounds on these symmetry-breaking features in linear and catalytic biochemical systems. Our bounds are independent of the kinetics and hold for both closed and open reaction networks. We also extend our results to master equations in the chemical space. Using our framework, we recover the thermodynamic constraints in kinetic proofreading. Finally, we show that the contrast of reaction-diffusion patterns can be bounded only by the nonequilibrium driving force. Our results provide a general framework for understanding the role of nonequilibrium conditions in shaping the steady-state properties of biochemical systems.