To get the recovery seed (the 24 words) back, do I need to create an additional, separate hidden wallet on the same Trezor, or do I need to do a factory reset? My hidden wallet is currently empty (no coins).
There is no way to get the seed words “back”.
You can factory-reset the Trezor and create a completely new wallet with a completely new recovery seed.
However, if there are any funds tied to the original seed, either in a standard wallet or in any hidden wallet, those will be irrecoverably lost.
It sounds to me like you managed to send all your funds away and your wallet is currently empty. If that is correct, then you can reset the Trezor and generate yourself a new wallet.