Allow private notes as inputs to `MockChain::build_tx_context`

[PhilippGackstatter]

Even though we did #1310, we currently can't easily build a transaction with private input notes, since the MockChainNote doesn't track enough information to create an InputNote:

https://github.com/0xMiden/miden-base/blob/8e88dc6b04429f67c685ce577f2afce6f8df757a/crates/miden-testing/src/mock_chain/note.rs#L13-L19

This is by design to mirror the privacy aspect of the notes. However, it would be great if we could pass a full private note into build_tx_context to be able to easily build a transaction with a private note. Currently, we use public notes exclusively, I think.

One way to do this would be similar to how we allow both a full Account and just an AccountId to be provided as input using TxContextInput. Analogously we could do:

pub TxContextNoteInput {
    Private(Note),
    Public(NoteId),
}

impl From<Note> for TxContextNoteInput {
  // Depending on the note type return either
  // TxContextNoteInput::Public(..) / TxContextNoteInput::Private(..)
}
impl From<NoteId> for TxContextNoteInput {
  // Return TxContextNoteInput::Public(..)
}

Then build_tx_context's signature can be changed to:

pub fn build_tx_context(
        &self,
        input: impl Into<TxContextInput>,
        note_ids: &[impl Into<TxContextNoteInput>],
        unauthenticated_notes: &[Note],
    ) -> anyhow::Result<TransactionContextBuilder> { ... }

We should also rename TxContextInput to TxContextAccountInput for clarity.

As part of this we should rewrite at least one test to use private notes as inputs. One candidate is settle_coincidence_of_wants.

cc @tomyrd in case I've missed how the above is already possible.

[tomyrd]

cc @tomyrd in case I've missed how the above is already possible.

In our case, we aren't using the build_tx_context to build and execute transactions in the client's unit tests so we didn't run into this problem. I don't think there's a current alternative way to achieve this behavior.