Is it permissible to use a free electronic application that acts as an imam for an individual's prayer, and is designing such an application considered a sin?

The questioner is sinful for abandoning prayer, and repeating short surahs is no excuse, for prayer is valid with Al-Fatiha alone and is not invalidated by omitting the recitation of a surah. Abandoning prayer is one of the greatest sins. As for the mentioned application, there is no need for it, as it distracts the worshiper from their prayer, and it might be taken as an imam in the future, so it should not be designed or published.