Most of the world's banks, whether big or small, are located in the US and Europe, In case of war, all banks will be closed, Which will immediately benefit Bitcoin, The price of bitcoin will increase infinitely, Many banks will quickly print dollars and euros to buy cryptocurrency quickly, This will have a huge impact on Bitcoin as there will be no other source for cross-border transactions. Remember that most of the world's banks are located in the US and Europe, while 20-25% of them operate in Asia and other regions.
Your prediction is so impractical because if a war starts between Europe and the US, not only banks will be affected. Most of the BTC nodes and Mining rigs are also placed in these two countries, so they will be affected by this war too. This means we might see fewer miners on the blockchain network but transactions might exceed the normal usage. Because banks will be closed and to make transactions they have to use something. However, due to fewer processing systems in the BTC blockchain, the network will become congested.
And we have to wait so long for our transactions to be confirmed. But in this scenario, the price of BTC will increase but it is so unlikely for BTC to reach 1$ billion because 1$ billion is not an easy target even if there starts a war and everything goes like you said, BTC will not touch that target.