My Google Drive quota is full, even though I’ve deleted my backups and cannot see anything using it

Here are a couple of things to check…

1. Note that your Google quota is not simply a “Google Drive quota”. It is used by other things in your Google account – including GMail, and Google Photos (which your phone might be automatically uploading to). More information from Google is available here.
2. If you send an item in Google Drive to the ‘Trash’ folder, then it still uses quota. You need to remove it entirely to get the quota back.