BUILD_ENGINE can be an empty database, as long as it has postgis installed. Would recommend you looking into postgis/postgis docker image, we use postgres 11 and postgis 2.5
for RECIPE_ENGINE, it's the same postgres database. and each dataset is loaded using the following repo (https://github.com/NYCPlanning/recipes), we have a cli tool that loads data into postgres and do some formatting, projection conversions & etc
we do not currently have a public version of RECIPE_ENGINE (it has a mix of public and non public datasets), however you can follow the instructions to build your own using https://github.com/NYCPlanning/recipes.
Let us know your use case, we can potentially create a dump for you
Is there an initial DDL script or a Postgres backup available to provide the initial structure for RECIPE_ENGINE or BUILD_ENGINE?