No. Your keys are generated on your phone and they stay there. We don't have a copy. Not a backup, not an encrypted one, nothing. Without the keys there's nothing for us to move, freeze, or hand over to anyone who asks.
What our servers do see is what any wallet's servers see: the transactions you've already signed, and the public chain data it takes to draw your portfolio. The app is a window onto the chain. The funds were never in the app. That's what non-custodial means in practice.
How that's different from an exchange
An exchange holds the keys, so an exchange can lock your account, pause withdrawals when things get busy, or go under with your balance on its books. Your balance there is a promise. On Aurus there's no promise to break. The SOL is on-chain, under a key only you have.
If Aurus shut down tomorrow
You'd be fine. Your recovery phrase is the standard format, so it restores in any Solana wallet. Your access doesn't depend on us existing. If it did, we'd be a custodian with a nicer app.
The thing we can't do either
The same design means we can't recover your wallet for you. Lose the phrase and the phone, and there's no ticket that brings it back. See what happens if you lose your recovery phrase and how to keep it safe. Ten minutes of effort, once.