Is it the motherboard or the battery?

I have an iPhone XR that I bought when they came out. Yesterday I noticed that my plugged-in phone hadn´t been charging and that it was on 1%. So i plugged it in using a different cable and adapter, but it still didn't charge. I tried restarting the phone, but the battery was too low so when I tried to power it on again it just showed the red battery icon. I then tried to clean the port and try again but only got it to show me the apple logo for a brief second before it all went black. The phone is now pitch black without any logo when I try to start it. I went to my nearby apple store to see if they could fix the problem. They told me that it wasn´t my charging port and that it looked to be dead. I was told that a repair would cost me about 500$ and that a new 12 or 13 iPhone would be better. I didn´t believe this and therefore went here to ask instead since I thought that it might be the battery since I hadn´t noticed any real problems with it before. So my question is really if the phone is basically unfixable or if a battery replacement or something else would work.