How can I use the API to find out the counts for virtual products and their respective granule counts?

Virtual collections (products) and granules define the additional attribute source_granule_ur. We can search for collections with that attribute and include granule counts.

Example: Here are the virtual product holdings in SIT.

curl --silent -g "https://cmr.sit.earthdata.nasa.gov/search/collections.xml?pretty=true&attribute[]=source_granule_ur&include_granule_counts=true&page_size=2000"

<results>
  <hits>13</hits>
  <took>30</took>
  <references>
    <reference>
      <name>ASTER L2 Surface Emissivity V003</name>
      <id>C1200056084-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L2 Surface Kinetic Temperature V003</name>
      <id>C1200056087-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L2 Surface Radiance SWIR and VNIR V003</name>
      <id>C1200056088-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L2 Surface Radiance TIR V003</name>
      <id>C1200056089-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L2 Surface Radiance VNIR and SWIR Crosstalk-Corrected V003</name>
      <id>C1200056090-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L2 Surface Reflectance SWIR and VNIR V003</name>
      <id>C1200056085-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L2 Surface Reflectance VNIR and SWIR Crosstalk-Corrected V003</name>
      <id>C1200056086-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L3 DEM and Orthorectified Images, GeoTIF Format V003</name>
      <id>C1200056092-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER L3 Orthorectified Images, GeoTIF Format V003</name>
      <id>C1200056093-EDF_OPS</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>ASTER Level 1 Full Resolution Browse Thermal Infrared V003</name>
      <id>C1000001579-EDF_OPS</id>
      <granule-count>2</granule-count>
    </reference>
    <reference>
      <name>ASTER Level 1 Full Resolution Browse Visible Near Infrared V003</name>
      <id>C1000001578-EDF_OPS</id>
      <granule-count>23</granule-count>
    </reference>
    <reference>
      <name>OMI/Aura Surface UVB UV Index, Erythemal Dose, and Erythemal Dose Rate Daily L3 Global 1.0x1.0 deg Grid V003</name>
      <id>C1000000020-GSFCS4PA</id>
      <granule-count>0</granule-count>
    </reference>
    <reference>
      <name>OMI/Aura TOMS-Like Column Amount Ozone and UV Aerosol Index Daily L3 Global 1.0x1.0 deg V003</name>
      <id>C1200055906-GSFCS4PA</id>
      <granule-count>2</granule-count>
    </reference>
  </references>
</results>