When I put water in the bathroom faucet, sometimes (but not always) I slowly started crawling into the overflow hole and then poured it back into the sink. The water includes black and gray black.
What confuses me is that even if this happens, the main drain works normally and the sink itself does not pour water or start to fill up (or at least not so obvious)
First remove the trap, place a bucket under the faucet (under the sink), then pour the water and see what happens. When cleaning the trap, make sure that there is no matted hair on it.
You should use chemicals carefully, because if you use chemicals, they may discolor the chromium around the sink. If you are not careful, they may also react with the pipeline in an unsafe way. They make some more organic gels, which can eat the safer use of organic wood logs (hair, etc.).
The overflow into the main drain is blocked. This is usually achieved by a small gap on the top of the tail wing, which is aligned with the overflow area in the gap between the inner and outer basin surfaces. Grease, hair and soap scum cum often collect around the plug assembly in the same area. Some of them will eventually pass through these slots. The area of the plug that attempts to remove debris will push more material into the slot, compacting the material into an impenetrable blockage. The main drain can work normally, but the overflow will only collect too much before it fills up and stops working.
The best way to clear the overflow blockage is to disassemble the drain assembly. Without these, a hard hook wire or similar tool can usually be used to mechanically clean the slot to a certain extent. Once loosened, the debris can usually be flushed into the overflow with tap water. Drain cleaners can also remove blockages, but I am concerned that the heat generated may damage the water basin. Bleach will kill the black mold that grows on this kind of thing, but it doesn't actually help clear the blockage.
Once the overflow port is working properly, the annoying things will no longer come out of the overflow port, but this does not solve the problem of how the water gets there in the first place. It will still flow there, but now it will inadvertently flow into the main drain.