My old paper wallet has a single private key, not a 12-word seed
You found a paper with a single private key and your wallet asks for twelve words: you won't find them, because that backup is not a seed.
**Old paper wallets store a single private key in WIF format —starts with 5, K or L, or with 6P if encrypted with BIP-38—, not a seed phrase: no set of 12 words reconstructs it.**
Why your paper doesn't have twelve words
Paper wallets from years ago weren't generated with a seed phrase. They held a single private key in WIF format: a string starting with 5, K or L. If encrypted with BIP-38, it starts with 6P. Source: Formato WIF + BIP-38.
That's why when you try to restore from seed, the wallet asks for twelve words and you don't have them. You didn't lose them: that backup never had them.
How to import a single private key
Instead of choosing “restore from seed phrase”, look for the option to import or sweep a private key (sometimes says “import WIF”). Paste there the key starting with 5, K or L.
If the key starts with 6P, you first need to decrypt it with BIP-38 using the passphrase it was encrypted with. Without that passphrase, the key cannot be used directly.
What happens if you can't decrypt a 6P key
If the key is encrypted with BIP-38 and you don't remember the passphrase, restoring from seed won't help: no set of twelve words reconstructs a single private key.
In that case, the problem is not the backup format, it's that you lost the ability to decrypt the key. Look for wallets that support BIP-38, but without the passphrase there is no way to unlock it.
No seed phrase does not mean the paper is useless
The fact that your paper holds a single private key does not prove your bitcoin are lost. It only means the restore method is not with twelve words: the WIF key is imported directly into a wallet that accepts private keys. If the key starts with 6P, it is encrypted with BIP-38 and you need to decrypt it before use.
Source: Formato WIF + BIP-38