ATmega328P-PU is commonly used in many projects where a simple, low-powered, low-cost micro-controller is needed. It is designed for use in industrial automation and home and building automation.
If you are building your own Arduino you will need to burn the bootloader. You may also have a malfunctioning bootloader and need to reinstall the bootloader.
Seriously, why are these Microcontroller units (MCUs) so affordable? If you search the internet, you’ll notice that the modern version of the design dates to the 1980s. However, these things will help you in moving from an Arduino Prototype into an actual PCB.