The text in the flysmart app has nothing to do with Airbus, it is an operator defined field. The procedure comes from your airline. Airbus has little or no knowledge of company specific EO SIDs.
As to calling mayday or pan, are you departing from a single runway airport, or a 2/3/4 runway configuration. If im going to cross the departure of another runway, it would be a mayday for me, there is a potential imminent danger of collision.
That would be one poorly designed EOSID, I would very strongly consider all other options before turning into known traffic, with or without a mayday! Either way, an EOSID that places you in imminent danger far greater than the original failure, is worthy of an ASR to the regulator.
Having said that, following all EOSIDS I have come across, I would call a mayday for the engine failure to begin with. That should alert ATC. Thereafter I will TELL them of my intentions. In that order.