OP: Your neighbors are assholes. But that doesn't mean they are entirely wrong, either. My rule is if the other side has a lawyer, you need a lawyer, too. That doesn't have to be your own personal lawyer; this is partly what homeowner's insurance is for, to understand what you are and aren't liable for, and to bring in lawyers on your side to push back against unreasonable lawyers/clients on the other side.
The primary issue that gives me pause is the stormwater runoff issue. Most states have rules that (a) require contractors to take action during construction to minimize stormwater runoff, and (b) prohibit people from making stormwater runoff worse on someone else's property. A house and driveway and all that is an impervious surface, so by definition adding that sort of thing will increase the amount of stormwater that runs off the property instead of being absorbed. So usually that means when you design a house, you need to do appropriate grading so the runoff goes into a stormwater sewer, and/or adding things like French drains to keep the water on your property.
This is why the stormwater issue concerns me. Because if someone messed up the design or grading, the stormwater could be an ongoing problem, not just a little construction runoff. And that's the kind of thing that can cost a lot more than $2K to fix.
Two other things to keep in mind on this. 1. Even if the contractor or architect or whoever is the one who screwed that up, you are very likely still responsible. It is your property, and you cannot contract away your responsibilities to your neighbors and the environment. Now, you may have a contract claim against whomever it is who screwed it up, but as far as the neighbors are concerned, they have the right to sue you, and to let you and the other guys fight it out over which one pays for the fixes. And 2. There are time limits here that you need to comply with. If you have home insurance that would cover the cost of any repairs and defend you, your insurance contract is going to require you to notify them within a short period of time, like 60-90 days -- and if you do not notify them in that timeframe, they can try to deny coverage! Similarly, if your contractor or architect or whoever screwed up, you probably have the right to go after them under your contract, but I guarantee that contract requires you to give them notice with an even-shorter period of time.
Now, on the other hand, this could all be complete and utter bullshit. But I always like to weigh the downside risk of the available options. Option 1, you report it to your homeowner's insurance and your contractor and anyone else you had a contract with related to the design and construction of the house, and you let them hash it out between themselves and the neighbors. Worst case, it's all bullshit. So your downside risk is that you made an unnecessary report to your homeowner's insurance. Oh well. OTOH, option 2, you don't report it, you talk to the neighbors, you try to deal with it yourself. Worst-case, they were right, your grading is wrong/your contractors never got the required permits/now it's going to cost you $20K to regrade and install a French drain.
IMO, the downside risk of option 2 far outweighs the downside risk of option 1. So if I were giving you legal advice -- which I cannot, because I'm not your lawyer and don't practice in this area anyway -- I'd tell you to stop talking to me and go bring in the experts who are paid to deal with this kind of stuff, bullshit or not. Good luck.