If it was created from Windows, then I guess your wallet was already compromised at that time using Windows. Because it's a rare case that your current Linux is infected if it was newly installed. Linux is considered more secure than the other OS, but it's not completely immune. If you don't randomly access any website with that OS, it should be clean, and I believe someone already has full control of your wallet since you created it from Windows OS.

For now, there's no way to recover those stolen BTC, but maybe since you already contacted Binance and they said they are going to refund stolen funds, it's worth trying.
However, I'm sure Binance will demand some data, including a sign message and your identity.