To develop galaxy-targeting approaches, the gravitational-wave community built a catalog of stellar mass in the local universe based on the Two Micron All Sky Survey (2MASS) spectroscopic and photometric redshift surveys. By cleaning and supplementing this catalog, the present work aims to establish a near-infrared flux-limited sample to map both stellar mass and star formation rate (SFR) over the full sky. The 2MASS spectroscopic and photometric redshift surveys are crossmatched with the HyperLEDA database and the Local Volume sample at d<11Mpc, providing a flux-limited sample with revised distance estimates and corrections for incompleteness out to 350Mpc. Scaling relations with stellar mass as a function of morphology are used to construct an SFR cosmography in the local universe. Stellar-mass and SFR densities converge toward values compatible with deep-field observations beyond 100Mpc. The 3D distribution of these two tracers is consistent with the distribution of matter deduced from cosmic flows. With spectroscopic redshifts available for about half of the ~400000 galaxies within 350Mpc and photometric distances with a 12% uncertainty available for the other half, the present sample may find applications in both cosmology and astroparticle physics. The present work provides, in particular, new bases for modeling the large- and intermediate-scale anisotropies observed at ultra-high energies. The distribution of magnetic fields at megaparsec scales, which can be deduced from the 3D distribution of matter, is inferred to be crucial in shaping the ultra-high-energy sky.