The iPhone 13 ran iOS 15 when Apple introduced it in September 2021. It has received four major updates (iOS 16, 17, 18, and 26) – and iOS 27 will make five.
In the past, iPhones have typically received between four and six major iOS updates before hitting "the end of the line", with no iPhone receiving more than six updates. iOS 27 is a bit of a surprise in that respect as it represents the seventh major update for iPhone 11-series phones and the iPhone SE (2nd generation).
As far as repair service goes, Apple normally stocks repair parts and offers repair service for five years after they stop selling a model. They discontinued the base model of the iPhone 13 in September 2024, so it won't become Vintage until September 2029. Service might be available, subject to parts availability, for a couple of years after that. In the specific case of battery replacement service, Apple is still offering that for the iPhone 6 - an Obsolete phone discontinued close to ten years ago.