Is there a centralized list of ArcGIS Python API functionality that will NOT work without also having access to Arcpy? It would be a great reference of understanding what is and is not possible without it.
None exists.
You could get started by comparing arcpy and shapely
You can search through the folder to find all the places where "has_arcpy" or "hasarcpy" show up. VS Code is great for searching w/ regex, since the formatting conventions aren't exactly consistent throughout the module.
A lot of false positives, though. Plenty of the functions just check if arcpy or shapely are present, i.e., is it a spatial dataframe or a "regular" dataframe. Also, it's not quite the same as "what is and isn't possible", since the shapely version will still attempt to do something similar.