House Listed And Disclosed As Sewer, It's Actually Sceptic. Do I Have Any Legal Recourse?

Hi all,

We just bought our first house and looking for info/advice about whether we have any legal options. The house was listed as being connected to the city sewer but it turns out its actually on septic and we are trying to understand if we have any recourse with the sellers/sellers agent or if we are SOL. We will be talking to our agent and a lawyer, but want to get as much information as possible. Location: South Carolina. What we know:

On the listing and on the sellers property disclosure they had said the house was sewer and reported no issues. There is a sewer cap in the front yard, and we didn't see (and still can't see) any kind of septic cap in the backyard. Our house inspector did not determine the the waste treatment system (thats absolutely on us). Move in, start to notice water pooling in a patch in the yard. This patch had previously been covered by a large burn pile, and we only noticed the water pooling once we have shoveled out the burn pile. Got a plumber round to determine what was causing the pooling and it turns out we are not connected to the city sewer, we are on septic, which is overflowing and causing the pooling. Cost to excavate and connect to sewer is going to be ~$10,000 not including anything that needs to be done to the sceptic tank (emptying etc).

With the porperty information sellers had a document of estimated utility costs and report paying $30 a month for sewer. I call the city and they say for this address they are providing water and sewer. I ask for documentation of sewer permit/ connection date, they cant find any. They send a crew out, and confirm it's capped off, we are not connected. Do we have any recourse at all with the seller/sellers agent as the house sewer was misrepresented? Or are we SOL because our inspector didn't check the sewer during due dilligence. If it provides any additional context, the sellers had a pre-inspection done, and this inspection does say that the house is connected to city sewer.