This could be described as $ifNull expression that accepts multiple arguments (rather than current two only). First non-null expression would be used.
It would be great if instead of making a long list of conditionals you could use any $any operator to get the first of the fields that exists.
This would make it easy to project an _id for use by a $group stage in situations where you have varied document schema.
For example, the next stage of the pipeline could be: