This won't affect anything one way or another, but I'm curious to know if the fingerprint sensor is working or not since it's built into the power button.
Anyway, although there can be several reasons for the power button not to work, the most obvious and the first thing to try is to replace the button itself. It's a mechanical component so it's susceptible to wear, plus it's on the outside of the phone so it's exposed to environmental factors such as heat, cold, humidity and liquids.
Sorry to say iFixit doesn't have a guide to that repair, but there's a Spanish site called Nadie Me Llama Gallina that has just what you need.
[link|https://www.nadiemellamagallina.com/en/manuales/smartphones-1/samsung-4/samsung-galaxy-a13-sm-a137-1378/flex-de-sensor-de-huella-y-encendido-12476|Manuals / Samsung Galaxy A13 SM-A137 / Fingerprint and power sensor flex|new_window=true]
The sensor itself is supposed to match the color of your phone, so you are expected to buy the right one, but of course the color is strictly cosmetic so any button will work. You can order them from any number of sites like Amazon, eBay and AliExpress. Double check using your model number because there could be differences between versions like the 4G vs. 5G models. Here's one for the 4G version that should work; it's just an example so do your homework.
[link|https://www.aliexpress.us/item/3256804169014129.html|Original Power Button Touch ID Fingerprint Sensor Flex Cable For Samsung Galaxy A13 - AliExpress|new_window=true]