If all you're doing to get this to charge is poking the plug a little harder, there is a better chance than not that you have something in the charging port or in the USB-C end of the cable. You say the cable is good, what are you basing this on? It works with other devices without this need to do any extra pushing, the cable looks good so it is good, it's always worked in the past so it's good? You also do not say if you have tried a different cable?
I'm not saying it isn't possible that the port is damaged, but a few things stand out that make me believe that it is not a damaged port. First USBC is sturdy. Nothing like micro-USB. Those things stopped working if you looked at them. Another thing is that it still charges just by inserting it as deep as possible. With micro not only did you have to get it plugged in deep enough but you also had to bias the cable up or down to get the contacts to touch the PCB. If you're not having to do this, it sounds like none of the solder points are broken. Literally you're just forcing the plug in place to reach the electrodes. I feel like you're maybe not seeing the debris.
Have you tried compressed air? Blow out the port and the plug end. Both are big lint magnets and once you pack it in there plugging and unplugging it the debris can blend in and hide. They are just big holes, and stuff ends up inside of them all of the time. Blowing from one edge of the opening across to the other side with compressed air might be enough to remove anything in there. On the flip side of that however is the fact that you have been compacting whatever is in there by pressing the plug in harder and harder.
You could also try something like a toothpick but I would be extremely careful. If you try this remember to be gentle, it's just a little lint or something.
Try a different cable. If you try a different cable that could tell you if the issue is the cable or the device. If two cables don't work you're looking for something in the device port, if one works and one doesn't, guess I don't have to finish that, but it's the cable.
Let us know what you find.