Broken time-reversal symmetry (BTRS) in superconductors is widely regarded as evidence for a multicomponent order parameter, yet the microscopic origin of the associated spontaneous magnetic fields remains unresolved. Sr$_2$RuO$_4$ is a central example, where BTRS has been reported by several probes, but its relation to superconductivity remains controversial. Here we use zero-field muon spin relaxation ($\mu$SR) to investigate how spontaneous magnetic fields evolve with pair-breaking disorder and crystal inhomogeneity in Sr$_2$RuO$_4$ [1]. We combine measurements on Sr$_{2-y}$La$_y$RuO$_4$ single crystals at ambient pressure with measurements on stoichiometric Sr$_2$RuO$_4$ under hydrostatic pressure, and compare these results with literature data spanning samples with different levels of inhomogeneity and Ru inclusions. We find that the superconductivity-induced enhancement of the muon depolarization rate, $\Delta\lambda$, decreases monotonically with La substitution and hydrostatic pressure, following approximately $\Delta\lambda \propto T_{\rm c}^2$ when the effective density of field-generating inhomogeneities remains nearly unchanged. In contrast, $\Delta\lambda$ is enhanced in samples containing stronger structural inhomogeneities, including nonmagnetic random disorder and Ru inclusions. These results support a picture in which spontaneous magnetic fields in Sr$_2$RuO$_4$ are generated by nonmagnetic inhomogeneities within a BTRS superconducting state, with the strength controlled by the superconducting order parameter. More broadly, our findings provide an experimental framework for interpreting local magnetic signatures in multicomponent superconductors.

1. Yongwei Li et al., https://arxiv.org/abs/2512.24585 (2025).