Just like a regular Cashu secret the script is blinded and only revealed to the mint when spending a token. However if you reuse keys all the time there is linkability
Discussion
But my question is more about the mint in having the full list of spent tokens, can they distinguish between tokens that were normal ecash spends and tokens that were script spends? Or do they look no different than any other spent token?
Yeah, the mint can distinguish between regular spent token and locked spent token. The proofs have a different structure, otherwise the mint would not be able to enforce the script