Jonathan Gagné, Leslie Moranta, Jacqueline K. Faherty, Jason Lee Curtis, Thomas P. Bickle, Dominic Couture, Amélie Chiasson David, Katie Christie, Samantha Lambier, Elise Leclerc, Livia Poliquin, Danika Belzile, Eric E. Mamajek

We present the Montreal Open Clusters and Associations database (MOCAdb), a public MySQL database with a Python interface. MOCAdb provides a census of memberships for 10259 associations and open clusters within 500 pc of the Sun, with a comprehensive compilation of literature measurements such as spectral types, kinematics, rotation periods, activity indices, spectral indices, and photometry. All known substellar objects are cataloged in MOCAdb, along with 2943 public spectra, to enable the characterization of substellar association members. MOCAdb also features periodically updated calculations such as Galactic UVW space velocities. We use this compilation to construct mappings between independent association definitions, and to update the BANYAN $Σ$ membership classification tool, which now includes 8125 associations. The BANYAN $Σ$ model construction is improved to account for heterogeneous and correlated errors and to capture complex association shapes using Gaussian mixture models. Combined with Gaia DR3, this enabled us to identify 11535 yet unrecognized candidate members of young associations within 500 pc, mostly M dwarfs. Our results corroborate a recent observation that systematics up to $\approx$4 km/s remain in Gaia DR3 radial velocities for A-type stars. We present an updated census of age-calibrated exoplanets and substellar objects: 134 age-calibrated exoplanet systems (plus 121 TESS exoplanet candidates), 99 of which did not appear to have known memberships so far, and 455 substellar (L0 or later) candidate members of young associations, 196 of which appear newly recognized. We bring the total of candidate isolated planetary-mass objects to 101, 53 of which are newly recognized candidate members.