For Bitcoin deposits to the "standard" wallet and Dash, LocalCoinSwap stores a minimum of 95% of deposited funds offline in cold storage. The private keys to these wallets have never, and will never face the internet. This ensures that they are safe from any nefarious actors.
All other wallets (ETH, BNB, USDT, USDC, etc.) on LocalCoinSwap are non-custodial, these are not managed wallets and all funds are secured by your own personal private keys that are only generated in your browser.