What is the correct number of angels with whom Allah reinforced the Muslims in the Battle of Badr, and why is there this discrepancy between one thousand, three thousand, or five thousand mentioned in Surat Al-Anfal and Surat Aal Imran?

There is no discrepancy between the two noble verses. Allah promised the Muslims at Badr a reinforcement of a thousand angels, then enticed them with an increase by saying, "following one another" (murdafeen), then increased them by three thousand, then by five thousand. This was to strengthen their hearts when they became apprehensive due to the large number of their enemy. The angels indeed descended on the Day of Badr and fought alongside the believers.