Hi Jay, just to clarify the standard arcpy site package shipped with ArcGIS Desktop and ArcGIS Enterprise is unrelated to the ArcGIS Python API.
The arcpy site package still holds its purpose in both Python 2 (ArcGIS Desktop/Enterprise) and Python 3 (ArcGIS Pro) for mapping, data management, analysis, etc.
The ArcGIS Python API, however, is designed for web GIS such ArcGIS Online/Portal for ArcGIS administration, analysis, content creation, etc.
ArcGIS API for Python | ArcGIS for Developers
"The ArcGIS Python API lets ArcGIS Online and ArcGIS Enterprise users, analysts, developers and administrators script and automate tasks ranging from performing big data analysis to content management and administration of their web GIS. The API integrates well with the Jupyter Notebook and the SciPy stack and enables academics, data scientists, and GIS analysts to share programs and reproducible research with others"
Simply put:
arcpy is for Desktop GIS application
ArcGIS Python API is for Web GIS application