@gerrycerryberry well.. most of reincarnation on the same world development is about knowledge right? i haven't seen back into old times that the mc got op power, except he finds a treasure place where he got last time on the pastfuture
Since he has those 13 years of experience he probably knows more spells than any other student and probably even the teachers. Plus that was his main expertise, since he could analyze and seal a dragon's magic in a very short amount of time, which is something even a 7 tiered magician couldn't do that easily or quickly. So even if he doesn't have the OP mana and artifacts anymore he can probably reach that again much faster, and until then he'll have his knowledge to take advantage of all the spells weak points. If he's sensible then he would also help his friends reach their power pre-reincarnation as fast as he/they can to make it much easier for them to prevent the extinction or near extinction of the human race.
@Etrius I had to check to be sure but you are mistaken, he did get into the school but into the commoner class so he wasn’t properly educated. In chapter 1 the mage says if he was in the tower of magic he would have been well trained. In chapter 2 he says he graduated from this school 10 years ago. So its likely that even if you lose in this part of the exam you can still get accepted if you do well enough in other parts.