Seem like the wallet is not owned by you
Why? because based on your explanation there has some "USDT" in the wallet and you tried to sent them. If the address is owned by you, most the time you connected to phishing site and the scammer will empty your wallet.
You find the wallet right on randomly internet with private key or seed ? the wallet has been set up by smart-contract, each time there has some transaction will automatically transfer to other wallet.
USDT in the wallet just the bait for people to send some ETH for the gass fee, is already old school scam method.
It is possible to have USDT in a wallet and don't have ETH. It is also possible that the wallet is not his and is a victim of a scam where someone put their private key in public with some usdt in it and seep any ETH deposits when someone try to move the USDT.
But I do not think @OP is a victim of that scheme since he is worried about someone sweeping all his tokens in that address.
I think your wallet is hacked, i faced problem as like that back in 2017. When i need to deposit eth for gas fee, but within few seconds it’s automatically transferred in another address before i move my tokens, i didn’t find any solution. Most provably your wallet is controlled by bot which is implemented by hacker otherwise how it’s possible to transfer within a few seconds.
Indeed this is what I am saying on my first reply in this thread.
You aren’t making sense just yet, what do you mean by immediately you transfer the Ethereum another person transfers it, do you mean when you transfer it another person immediately transfers that same Ethereum away from your trust wallet account?
Well I think it maybe from someone who you have ignorantly allowed access to you account. Rather than trying any further why not create another trust wallet and transfer the Usdt from the old trust wallet into it.
He can't do what you are suggesting him to do since ETH meant for gas fee is emptied out a second after it is confirmed.