Theoretical proposals to reach the Heisenberg scaling of the measurement precision typically require carefully engineered interactions or initial entanglement. In studying optical magnetometry, we show that the continuous collective measurement process itself can generate the necessary many-body quantum correlations to achieve the elusive Heisenberg scaling of the quantum Fisher information in a dissipative, steady-state system without direct inter-atomic interactions. By contrasting a correlation-neglecting but otherwise consistent semiclassical model, which can formally violate the quantum Cram'er-Rao bound (QCRB) by several orders of magnitude due to the invalid separability assumption, with a collective quantum model, we isolate measurement-induced correlations as the essential mechanism. The violation of the QCRB serves thereby as a fundamental sanity check for semiclassical spectroscopic theories. \textcolor{}{This work reveals correlations induced by a collective quantum measurement as a widely unexplored quantum resource for quantum-enhanced sensing, and suggests a new paradigm for achieving Heisenberg scaling in dissipative states of open quantum systems without relying on sophisticated quantum operations.