How does wallet restoration work? If the device is offline/cold storage, how does it associate your wallet with your seed phrase

Example:

You have a Trezor hardware wallet with a seed phrase. You lose the wallet, or it's destroyed.

You purchase a new hardware wallet from Jade. You restore your wallet using your seed phrase from the Trezor device.

How is this possible if the devices are offline? I don't understand how a wallet is associating your seed phrase with your wallet if it has no internet connectivity.