I am looking to write a server application to upload files to Google Drive. I was previously using the Documents List API, but I see that is deprecated. I\'d like to move to the
Your application needs the user's permission to use the API against his files. That authorisation needs to happen using web based Oauth. The result of that authorisation is your server app ends up with a refresh token, which it can store. At any time, your app can convert that refresh token to an access token and access the drive files.
So, provided you accept that you need to do a one-time authorisation, you can achieve what you are looking for.