Yes it is extremely over-saturated in most US States. California is probably one of the worst and Florida has extremely stringent restrictions. It is best to spend time checking out local markets and craft fairs to get a feel of how many are around. Selling online is extremely hard without spending a large chunk of your time promoting, and in my opinion forget Etsy. Do a search on Etsy for handmade soap, that should answer you question. Do Not expect to make much money, some nights I leave my largest market with 20 bucks in my pocket and that is without having to pay booth space. It is a lot of work
Have you any business experience? If you don't have much experience in small business, it's time to get educated or find a partner who knows the ropes. A small business is a hard life and requires a wide variety of skills, flexibility, good management ability, money, and long hours of work.
What kind of soaping experience do you have? If very little to none, now is not the time to be thinking about soaping as a business venture. Soap as a hobby first, and then after a year or two when you have your skills built up, some good reliable recipes, and know you are serious about it, then would be a better time to decide if you are passionate enough to expand the hobby into a business.
Have you researched your local area to see what other soapers have businesses in your area? It doesn't matter if one area is oversaturated if you live in an under-served area ... and vice versa. But I will say that if you expect to make a fortune selling soap or other bath and body products, whether locally or on line, you may want to think again.
A tip -- don't cross post the same question to different forums. Pick one forum and post once.
I think it is a nice idea if you already have someone wishing to buy your soap ( I mean a mediator ), or you have some significant budget for promoting+business experience. Anyways, sometimes a huge motivation and desire make miracles Good luck!