So here’s an update on how I “solved” my problem (thanks to @OldRoutard advice!:
After getting some isopropyl alcohol, some cotton buds and a suitable screwdriver, I opened the phone and cleaned all the contacts. Although the problem was apparently solved after that, there were a couple of weeks where the charging was still unreliable (it switched from slow to fast several times, and sometimes didn’t recognise the charger); however, it charged much better than before the cleaning (as where at best it would only charge 15%/20% in 8 hours). Now, and for the last two weeks, it detects the charger and it is charging perfectly… let’s see how long it lasts like this 
P.S. I bought some covers for the USB-C port, to prevent any more dirt or moisture getting into the contact from now on. I hope this will extend its lifespan.
Parts of the phone drying after cleaning them
One of the main problems I had during this process is that, as I had to open the phone other several times, I have several stripped screws, and it was very difficult to open it. Do you know where I can buy the screws for the Fairphone 3? It would be ideal if they sold them in the FP shop.
By the way, a few days ago the screen wouldn’t turn on properly when unlocked, it was at a much lower minimum brightness than the normal minimum brightness, and the screen was flickering. After fiddling with the phone and tightening it I managed to get the screen to work normally again, but this happened many times on that day… I hope it’s nothing serious and it’s simply because the screws are not too tight… but the truth is that I’ve had a few problems lately with my Fairphone 3 
@Lena_Ka, have you been able to solve your problems by cleaning the port too? Or have you replaced it completely? I’m thinking of doing it if it fails again, but I’m afraid that I won’t be able to open it because of the problem with the screws…