So your mnemonic phrase must be for your BNB wallet then. Or is it one seed for all cryptocurrencies in your wallet? Please clarify this.
With what I have just checked recently, the mnemonic to TokenSwap wallet is a BIP39 seed phrase, I also install, delete and reinstalled the wallet. When I install it at first, I copied down the seed phrase, the Bitcoin address and the ethereum address generated. I found out that the mnemonic is BIP39, then I deleted and reinstalled back the wallet. The wallet regenerated me the same Bitcoin and Ethereum addresses also.
There is export private key and keystore option. Im learning the hard way I shouldve save them before uninstalling the app..
You do not need any export key for this, so far you have your seed phrase to the wallet. I tested it for Bitcoin and Ethereum, it has the same derivation path to your addresses. I couldn't find the option for binance coin but the derivation path will also be the same. That aside, also you restored the seed phrase on the same wallet which is TokenSwap, which should not be a problem, there is nothing wrong with your wallet. If you used the right seed phrase, it will generate all other seeds, private keys and addresses needed. The addresses that store your funds will also be generated along.