We explore the role of redshift-space galaxy clustering data in constraining nongravitational interactions between dark energy (DE) and dark matter (DM), for which state-of-the-art limits have so far been obtained from late-time background measurements. We use the joint likelihood for prereconstruction full-shape (FS) galaxy power spectrum and postreconstruction Baryon Acoustic Oscillation (BAO) measurements from the BOSS DR12 sample, alongside Cosmic Microwave Background (CMB) data from Planck: from this dataset combination we infer and the lower limit , among the strongest limits ever reported on the DM-DE coupling strength for the particular model considered. Contrary to what has been observed for the model and simple extensions thereof, we find that the combination returns tighter constraints compared to the one, suggesting that there is valuable additional information contained in the broadband of the power spectrum. We test this finding by running additional CMB-free analyses and removing sound horizon information, and discuss the important role of the equality scale in setting constraints on DM-DE interactions. Our results reinforce the critical role played by redshift-space galaxy clustering measurements in the epoch of precision cosmology, particularly in relation to tests of nonminimal dark sector extensions of the model.