Is it obligatory to make up the Fajr prayer if one relied on a later timing from two prayer applications, and it became clear that most other timings precede this timing?

If you did not know that you ate after dawn according to the later calendar, then you are not required to make up for it; because the original state is the continuation of night. And whoever ate doubting the advent of dawn, his fast is valid according to the majority of scholars, and one may eat until he is certain of the advent of dawn. As for prayer, pray according to the later calendar to ensure that the time has entered.