It's only a pan pan pan because almost every airliner can fly on 1 engine. An a380 can climb and maintain an altitude on one engine, albeit much slower and much gentler. Mayday means you have radio priority, meaning nobody else can talk. To call a Mayday in a survivable situation can cause heavy fines.
froggie767 Losing an engine is a mayday emergency especially at a critical stage of flight I.e after take off. They will be given immediate priority to return to the field.
It has always been "pan-pan, pan-pan, pan-pan". It's just the Americans have never really recognised or acknolwegded that phrase fully since its conception.
The Capt. requested the F/O to insert the "Hold" at PAS to comply with the published "Engine Out SID", Holding at 4000 feet. In this demonstrative example, rather than activating a prepared EOSID; "Secondary Flight Plan" in the FMGC, the F/O simply made a lateral revison at PAS sequencing a "Hold" for the aircraft to enter. This is done to allow the crew to follow ECAM Actions and handle the emergency safely. In real life, once resolved, vectors for approach to land would then be requested.
A mayday distress call should be made if the aircraft is in imminent danger, in which case, it was under control and no imminent danger existed. However, the captain got the pan pan call wrong... it's "Pan pan, pan pan, pan pan" and not "Pan pan pan".