Can I directly record a video in iCloud Drive (/Google Drive)? By record, I mean record a video using the option available in the Control Center. If I am running out of the local storage space, can I record (upload?) directly to the Drive? If not, is there a solution?
No, the built-in Camera app does not support recording directly to iCloud Drive or Google Drive.
A third party app could record directly to the cloud - similar to how apps like Facebook does live streaming that is not recorded in local storage, but only transmitted to a server (that you could then store it in cloud storage).