Grab a thin needle or piece of wire, thin enough to easily insert into the USB-C port, and scratch all of the dirt and lint out of it. Always point the needle towards the outer surface so you don’t scratch the electrical contacts in the middle.
There is often a surprising amount of junk inside even if you can’t see it from the outside, and that can greatly affect the connection quality.
My phone recently had a similar issue where it would only charge if the cable was inserted in a specific way, and any movement would cause it to stop charging. The cable also wasn’t really held well even though it looked like it was fully inserted. I cleaned out the port even though I couldn’t see anything inside, and managed to pull out a bit of dust anyway. And now my phone no longer has charging issues and holds on to the cable much better.
USB-C unfortunately just seems to have a design that makes it very easy for dust to get stuck in it, while also having a relatively low tolerance for foreign material buildup before the connection quality gets affected, making this a quite common issue.
A wooden toothpick is probably a bit too thick. You’d want something thin enough that it can be inserted without touching the electrical contacts. If you do have something plastic then that’s probably better, but if you do the cleaning when the device is off the USB port should be unpowered and there shouldn’t be a risk of causing a short, and modern USB ports are quite well protected again shorts anyway so it’s very unlikely to cause damage just by being conductive. You mainly want something that is long and thin enough to get all the way to the bottom of the port without having to apply any force. If the only things you have that are long and thin enough to reach the bottom of the port without having to be forced in are made of metal, then that’s still a safer option than jamming something too thick into the port that can deform the center contacts.