How to add new field with constant using $project?

from doc:

The $addFields stage is equivalent to a $project stage that explicitly specifies all existing fields in the input documents and adds the new fields.

But if I write:

db.projects.aggregate(
        {
            $project: {             
                count: 1            
            }
        }  
)

This code doesn't add count to the result.

In contrast:

   db.projects.aggregate(
            {
                $addFields: {               
                    count: 1            
                }
            }  
    )

This adds count field to result.

How to add new field to result using $project? I think it is possible because it is equivalent.