Does the wallet software use the Bip32 derivation paths to generate the partial signature map?
The PSBT comes with the witness script. The witness script contains derived public keys with no information about their origin. The derivation paths in the PSBT tells the signer:
- What extended key was used to derive each key (does it belong to the signer?).
- What path from the extended key was used to derive it.
It is useful for the signer to be able to sign (by deriving the corresponding private key) or to check the change output (by re-constructing the script from trusted data).