Hi Seb,
The PVWatts V6 API should give results consistent with the PVWatts Online Calculator. It uses a different set of weather files than the endpoint you mention below, which is current data available from the NREL National Solar Radiation Database (NSRDB). If you use pvwattsv5 with data from the NSRDB you will get different results than from the PVWatts V6 API.
The PVWatts V6 API does include time stamp and weather data in the hourly outputs along with the latitude, longitude, and elevation data required for sun position calculations, so you could use that to either construct a weather file in the SAM CSV format to use with the 'solar_resource_file' input to pvwattsv5, or to pass data as a table to the 'solar_resource_data' input. Note that the time zone is also required, so you would have to provide that as well.
Best regards,
Paul.