A common environment acting on a pair of qubits gives rise to a plethora of different phenomena, such as the generation of qubit–qubit entanglement, quantum synchronization, and subradiance. Here, time‐independent figures of merit for entanglement generation, quantum synchronization, and subradiance are defined, and an extensive analytical and numerical study of their dependence on model parameters is performed. A recently proposed measure of the collectiveness of the dynamics driven by the bath is also addressed, and it is found that it almost perfectly witnesses the behavior of entanglement generation. The results show that synchronization and subradiance can be employed as reliable local signatures of an entangling common‐bath in a general scenario. Finally, an experimental implementation of the model based on two transmon qubits capacitively coupled to a common resistor is proposed, which provides a versatile quantum simulation platform of the open system in any regime.