Then you don't know how long that phone had been sitting on a shelf not being charged. iPhone 13 was released in 2021, almost 3 years ago. If that phone sat around not being charged, its battery health was already degraded by the time you got it. Lithium iON Batteries which are not charged for extended periods of time lose battery health.
Let's see what it shows for warranty, by going to Settings > General > About and look at the box under Serial Number. Tap it and if my assumption is correct, the phone's warranty may have already expired. iPhone warranty begins the day an iPhone leaves Apple or an actual Apple Authorized Reseller. A gadget shop is not an authorized reseller.