The LHAASO observatory has recently measured details of the cosmic-ray (CR) spectrum in the knee region (1-10 PeV) with unprecedented precision, including its average CR mass composition and the spectrum of the proton component. We use these precision measurements, combined with direct measurements of CRs by space-based detectors, to derive predictions for the spectrum of diffuse 7-ray and neutrino emission from the interstellar medium under the assumption that the CR spectrum is universal throughout the Milky Way. We compare these predictions with the Fermi-LAT and LHAASO measurements of the diffuse 7-ray flux from inner and outer Galactic plane regions and with estimates of the neutrino flux based on the IceCube data for the same Galactic plane regions. We notice that the model predictions exceed LHAASO 7-ray measurements at energies above 100 TeV. This excess can be interpreted within a CR knee model assuming a "local PeV CR bubble." Within this model, we infer the extension of the local PeV CR bubble of 1.1 + 0.2 kpc in the direction of the inner Galaxy and of 0.5 + 0.3 kpc toward the outer Galaxy.