When Maurice stated in War "I thought we were the only ones", when the audience was introduced to Bad Ape, should have been the new premise of the movie. It could continue along the time-line that Kingdom was set in, but an entirely different location, such as New York to show continuity for the original 1968 version. These apes would have no knowledge of Caesar nor the legacy he created.
It would have explained the different clan. And why these humans were different.
I would have been curious to see what leadership and morality these apes would have had.
It was a decent movie, but I as a fan wanted more. A new legacy. Perhaps merging the two in the future.