Is there a copy of the OSM API anywhere (either at OpenStreetMap.org or elsewhere) either with rendered maps based on the data added or with the planet files/diffs output that someone could use for rendering?
Is content at Downloading data - OpenStreetMap Wiki answering your question?
I’m not quite sure what you are looking for.
There are several available APIs (e.g. Databases and data access APIs - OpenStreetMap Wiki) if you’re looking for specific instances of them. Or are looking for source code for them? (in which case OpenStreetMap on GitHub · GitHub might be of use). Or do you want dumps of raw data? (in which case see @Mateusz_Konieczny answer above). You could render that data using a number of renderers (e.g. Rendering - OpenStreetMap Wiki - each with their own source code and usage instructions), if that is what you want.
Or do you need something else? https://switch2osm.org/ might be of use maybe.