Is it obligatory to make up the days when the breaking of the fast was delayed until the time of the Maghrib prayer's takbeer, knowing that the time for Maghrib had not yet passed?

Breaking the fast early is a Sunnah (recommended practice), not an obligation, by the consensus of scholars. Delaying it for the purpose of supplication does not invalidate the fast nor does it necessitate a make-up fast, but it is contrary to the Sunnah.