We have mapped the number density and mean vertical velocity of the Milky Way's stellar disk out to roughly two kiloparsecs from the Sun using Gaia Data Release 3 (DR3) and complementary photo-astrometric distance information from StarHorse. For the number counts, we carefully masked spatial regions that are compromised by open clusters, great distances, or dust extinction and used Gaussian processes to arrive at a smooth, non-parametric estimate for the underlying number density field. We find that the number density and velocity fields depart significantly from an axisymmetric and mirror-symmetric model. These departures, which include projections of the Gaia phase-space spiral, signal the presence of local disturbances in the disk. We identify two features that are present in both stellar number density and mean vertical velocity. One of these features appears to be associated with the Local Spiral Arm. It is most prominent at small heights and is largely symmetric across the mid-plane of the disk. The density and velocity field perturbations are phase-shifted by roughly a quarter wavelength, suggesting a breathing mode that is propagating in the direction of Galactic longitude l similar to 270 deg. The second feature is a gradient in the stellar number density and mean vertical velocity with respect to galactocentric radius. This feature, which extends across the entire region of our analysis, may be associated with the extension of the Galactic warp into the solar neighbourhood in combination with more localised bending waves.