Allow completing partial notes in private
So far in our apps partial notes are used by a single party, i.e. in the AMM it is the same actor that creates and completes (their) partial note. If the note was completed by someone else (e.g. in an orderbook DEX), then we may wanto to allow said completion to happen privately.
The reason is that this second actor would likely want to remain private, and not being able to do private completion would require that they (e.g. in the case of the orderbook) transfer tokens privately to the contract, and then have the contraact publicly complete the note. Private completion would not just remove these storage accesses (and associated DA costs), but also reduce the AVM burden, leading to lower tx fees.
Implementing this would require searching for the partial note completion log in private as well, which might be annoying due to issues related to https://github.com/AztecProtocol/aztec-packages/issues/11639, including https://github.com/AztecProtocol/aztec-packages/issues/10273.