Would the tin peptide nail renewal improve or strengthen existing nails, or would it only work on new nail growth?

The effects seem to be rather fast - in about three weeks which is too fast for new nail outgrowth.

The nail bed has some action on nail health. Damage to the nail bed causes nail damage. The nail plate is held together by strong, interconnecting bands of protein fibers, and is kept flexible by a sticky residue of oils and moisture that constantly flow upward from the nail bed.