I had a similar problem. When I plugged in my USB-C cable into the Pixel 3XL it would sometimes charge and depending on a slight change in angle it would sometimes charge. I also had a crack in my screen so I ended up ordering both a screen and a USB-C replacement parts from iFixit. If your screen is not broken it’s a bit difficult to remove the back and/or screen on this phone. I would recommend just buying a wireless charger. But if your up to the challenge, replace the USB-C assembly which is fairly inexpensive. I would HIGHLY recommend a good heat gun or blow dryer to heat the edges of the phone and more easily remove the back and/or screen.
P.S. I also talked to Google about the USB-C issue and they would’ve replaced it if the screen was not cracked. After checking how much a ‘certified’ replacement would cost I decided to replace BOTH the screen and the USB-C connector for about 150 bucks less. (I already have the iFixit toolkit and have done similar fixes)