Calibre Companion can be used to access the
replica of your library you have on Dropbox, but not Google Drive.
First see this ==>>
I am getting errors with my calibre library on a networked drive/NAS?. Cloud storage services like DropBox, OneDrive etc are effectively networked drives - so care is needed. And as you'll read there Google Drive and calibre are incompatible.
Then see this ==>>
Calibre Companion - Cloud Connection
BR