Youre lucky they replied you, hope they have given you the 2fa and youre now able to log back into your account. Next time you should try to write it down, maybe on a shit of paper and keep it somewhere safe so that you wouldnt lose it in case. If its not going to be safe on a sheet of paper you can save it on Keep mobile Note or any of those you get on your phone like Microsoft note and such and backed up, in case you need it later you can take it from there.
Binance has a good service and staff when it comes costumers issues, I don't think why they did not resolve that issue that OP said. Probably that problem was very risky for them it needs more time to recover, I don't know a week(s) or more worst if month(s). So, this mistake made us have a lesson, our responsibility to keep our back up seed safe because that is money that we must be careful when making a transaction online.