Water pump replacement

I had replaced my water pump about 2 to 3 years ago. This past winter, I did not drive my car (328 xdrive) and the battery died. I bought the ctek charger and was able to bring the battery back to life. However, these radiator fan started kicking on very high upon starting the car. After a day or two I started getting warning lights for high temperature. Scanning with the Carly app it said that I had two faults for the water pump. I’m just curious are these water pumps known to fail if the battery goes flat?

Since I started to work from home in the beginning of 2025, I barely drive the car. Between then and now, I think I’ve only driven 800 miles on it.