/ AbstractBlazars, supermassive black hole systems (SMBHs) with highly relativistic jets aligned with the line of sight, are the most powerful long-lived emitters of electromagnetic emission in the Universe. We report here on a radio to gamma-ray multiwavelength campaign on the blazar BL Lacertae with unprecedented polarimetric coverage from radio to X-ray wavelengths. The observations caught an extraordinary event on 2023 November 10-18, when the degree of linear polarization of optical synchrotron radiation reached a record value of 47.5%. In stark contrast, the Imaging X-ray Polarimetry Explorer (IXPE) found that the X-ray (Compton scattering or hadron-induced) emission was polarized at less than 7.4% (3sigma confidence level). We argue here that this observational result rules out a hadronic origin of the high energy emission, and strongly favors a leptonic (Compton scattering) origin, thereby breaking the degeneracy between hadronic and leptonic emission models for BL Lacertae and demonstrating the power of multiwavelength polarimetry to address this question. Furthermore, the multiwavelength flux and polarization variability, featuring an extremely prominent rise and decay of the optical polarization degree, is interpreted for the first time by the relaxation of a magnetic "spring" embedded in the newly injected plasma. This suggests that the plasma jet can maintain a predominant toroidal magnetic field component parsecs away from the central engine.