Is there any way to find the video editing software or camera that created a video?
Different NLEs each seem to live in their own metadata world.  One common metadata element they all seem to preserve fairly well is timecode.  Almost all support a few common elements, such as REEL, SCENE, and SHOT.  But DaVinci Resolve, Premiere Pro, and Final Cut Pro X each have metadata slots that are unique to them, even in cases where the metadata slot shares a common name.  MPEG, Quicktime, and other media formats do have slots for metadata, but nothing like the expansive and consistent world of EXIF.

In the pro video world, metadata is usually entered first via a slate, with the camera shooting the actual metadata at the start or end of a shot, and then what is now called the DIT (director of Imaging Technology) translate the slate data to metadata for the project.  Some digital slates actually create little databases so that at the end of the data, all the text the camera shot as video footage is also available to be uploaded to a (metadata) database.