So I should (a) not care about personal identity over time, even if it exists, and (b) stop believing that it exists.

That sounds like a thought-stopper. What is the utility of the belief itself? What predictions can we make if personal identity exists? What is the maximum set of incremental changes you can make to yourself until you stop being "you"? What is the utility of being "current you" as opposed to "optimized you", and which "you" gets to decide? What is the utility of being "you five years ago" as opposed to "current you", and which "you" gets to decide?