How to clean bathroom sink area where overflow water goes?

Hi there! Perhaps this will help. https://homeguides.sfgate.com/rid-smell-bathroom-sink-overflow-44941.html

Use a baby bottlebrush. It has a dual tip. Try that. Use some 409 in the hole and on the brush. Please use eye protection when doing that.

I make a cone out paper and pour baking soda down the hole. Then pour vinegar down. It will foam and a lot of crud will come out.

This "crud" is from soft soaps, shampoos, hair, toothpastes, etc. Follow William's advice. After 45 minutes, carefully pour a large container (several quarts, minimally) of boiling water down the drain hole. Repeat several times. Use QTips to remove remainder.

I'd recommend putting baking soda down the hole then trying to pour distilled white vinegar. You can also buy cleaning brushes that are bendable. Maybe try using a bendable brush to clean it afterwards.

I have been using vinegar with an old toothbrush but I think William's idea is much better.

Here is how I clean mine https://chascrazycreations.com/clean-bathroom-natural-products/