Trust wallet is a non custodial wallet where they will give you private key, you can use this private key (from Trust wallet) to access your wallet through any other non custodial wallet e.g.
Trust wallet is not open source and it is a big issue, maybe not now but in future, who knows?
A big warning is from Atomic wallet.
Atomic Wallet hacked! Get your funds out now!You will not always have chance to get your funds out if a wallet is compromised like that.
As for TRC20 wallet, it's same, you just need to find and use non custodial wallet.
Most EVM-compatible wallets will start with ERC20 chain first and move to other chains like BEP20, TRC20, ...
Custodial wallet e.g. centralized exchange is where you must avoid to leave your coins because if they're disappear, your coins also disappeared too e.g. Mt.Gox, FTX etc.
Put our your funds to exchanges then you only can pray that they will not be hack or scam you.
Reminder