Citizenship is irrelevant to US customs. Residency counts. US Citizens who are non-residents are treated the exact same as other non-residents.

That said, the alcohol restrictions are the same for all persons entering the US, regardless of where you reside. What changes is the $ limit of non-alcohol/non-tobacco goods you can bring in.

US Resident with 3 bottles of €200 each wine:
3x750ml = 2.25litres, so you would be liable for import duty on 1.25litres. This is about 3% plus misc. admin fees. The fact that you have not gone over your exemption in $ terms is irrelvant for tobacco and alcohol.

Watch out for the state you are going to as there may also be laws there limiting what you can bring in, and your 10+3 bottles could be an issue, especially if they are half-litre bottles of beer.

Assume €4/bottle for your beer and €10/btl for your wine. You would be looking at about $2 in duty and another $2 in excise tax. No idea what the processing/admin fees would be.