iPhone 13 probably end support earlier than 14, I don’t think they want to stop support all A15 iPhones at the same time. However, since iPhone 13 is the last iPhone with 4G RAM, it may not perform well compare to 14 in the future.

If you need to replace battery under Apple Care, the battery health has to lower than 80% or you pay for the battery replacement by yourself. I guess you may want to pay for another year for now since a refurbished iPhone 13 Pro still costs a lot now.

iPhone 13 Pro/Max is better. It has A15 chip, 120Hz screen. The difference between A15 and A16 is small, iPhone 13 Pro also supports portrait focus change. The only thing is the 3X telephoto camera is not great in low light condition.