Yes! You — and only you — control the private keys in your Trust Wallet.
Your private keys (all derived from your recovery phrase) never leave the Trust Wallet app. The only way to get them out is when you reveal the recovery phrase. So handle it with great care!
No-one, not the Trust Wallet team, not the backend, not any of the DApps or other mobile apps, no-one can access to the private keys from your wallet. Whenever an operation is needed that requires the private key, Trust Wallet only signs a message with the private keys, without revealing it.
Your recovery phrase is the master password for the private keys. If you have different currencies (BTC, ETH, BNB, etc.) in your multi-coin wallet, each has a different private key internally, all derived from the recovery phrase. Is is possible to recover these private keys? Trust Wallet does not support extraction of the internal private keys, but they are derived from the recovery phrase using industry-standard methods, also used by other wallets (there are even some tools for deriving the private keys off a recovery key, such as iancoleman.io/bip39).