Ohhhh good point. My tired brain isn't wired enough to make sense of this rn esp with the translations often being so-so.
I am guessing after re-read it must be either a translation error or his children weren't official heirs for a while because in chapter 9 they indeed say "the late emperor had 5 sons and 1 daughter," all from different mothers (so, maybe the emperor didn't have an empress, and only concubines?) The ML is mentioned as being the emperor's "half-brother" in chapter 1 or 2, and in chapter 9 they say he's the youngest son and full sibling of the (late emperor's) only daughter (meaning, that he and she were the only siblings sharing both the same mother and father)
"An emperor without heirs"? That would mean the ML's older bro, the current emperor, wasn't the former emperor's son.