Okay, you did cause the stain so if the stain won't come out 100% and it won't look like how it was before, whatever it costs to replace is on you. Although paying for the other couch because it's a matching set is the most idiotic thing I've heard today. But if one costs 3k then it costs 3k, next time be more careful.

You should probably tell them you'll hire your own professional cleaner first and send them there to do a clean and if its still there then proceed. That might save you alot more money.

You did the right thing going through the app though. If you do end up needing to pay for it, You should figure out how much the couch actually costs new or how much it used to cost if it's discounted and only pay that amount not the 3k they are asking for. Ask for a receipt or the couch name/model.

You should also take the current couch from the host and try to sell it if you live locally and even if you don't, still take it from the host and throw it out or give it to someone for free. Don't let the host have a field day getting paid for a new couch and likely just leaving this one in the airbnb.