That sounds like it's either broken or there's some dust or lint in the plug/cable.

Google is usually pretty good about their USB-C implementations.

Of course it's broken. It also won't power on unplugged, even with a full battery.

Definitely not googles finest device.

might be a cheap cable.

I had a similar issue on my old phone and I'm pretty sure it was because of something wrong with the connector on the phone's side.