The translation_entity module added the concept of a "default_operation".
It is only used by User (which has 'profile' and 'register' instead of 'add' and 'edit').
While #2014821: Officially introduce form modes wants to continue to use the 'default' operation, #2006348: Remove default/fallback entity form operation plans to remove that.
The compromise is to make 'default_operation' more widely used and/or mandatory.