So I just installed iOS 9 GM on my 6+ and it is running slow and delayed at pretty much every action. Is this because iOS 9 is running some sort of indexing or background setup process?
Could be. Give it a day to sort out and charge and see how it feels. It can take a bit at first. If it continues, consider the 9.1 beta that's out. It's been fine so far.
It does this every new update, at least the major ones. People report awful battery life and sluggishness immediately after updating, but it's always because of indexing.