This OctoPrint plugin moves the webcam stream from the controls into its own tab. Keyboard control is still possible and it is compatible with the FullScreen Plugin.
This plugin can be installed via the bundled Plugin Manager or manually using the URL below. More information on how to install a plugin can be found on the OctoPrint website.
https://github.com/malnvenshorn/OctoPrint-WebcamTab/archive/master.zip