It's used instead of a public key or an address.
It's used
along with the public key, to verify the ownership.
My issue is whether this signature can be used for several transactions.
It can't, because in each transaction you need to include the input, which is the id of another transaction (and many other values[1]). Each transaction is unique due to this identifier, which is the id (AKA TXID or transaction hash). You can't have the same signature, because you need to sign an entirely different message each time.
[1]
https://learnmeabitcoin.com/technical/transaction-data