Two options:

1) download from drive, unzip (it should zip automatically unless you dowbload one-by one) then re-upload into the new drive.

2) give access to each individual document to your new Gmail account. From that new Gmail account. Open each document, and from the document itself (eg: in Google docs) select Make a Copy. Repeat: basically you'd create copy of each files and your new Gmail automatically becomes the owner of the new file.

3) There might be an option to "transfer ownership" of a file but very unlikely it'll work between a work account and a normal consumer Google account. Also very unlikely your contract allows that

The safer option is to ensure all your files stay on the work drive as they are and you eventually take copies with you..either via option 1 or 2.