You can create a draw.io diagram in a specific Google Drive folder by selecting that folder in the Drive interface,
pressing the new button, then select "More...",
then select draw.io Pro.
The new diagram will be created in that folder.
You can move existing diagrams either in the Drive interface by right clicking the diagram and selecting "Move to...:
Then selecting the destination folder.
Or, within draw.io, select File->Move To Folder:
and then select the destination folder.