feat(public_executor): allow access to the commitment trees in public execution

[Maddiaa0]

Description

CommitmentsDB interface has been added to both executors, I have chosen not to completely unify their implementations as private goes through an aztec node while the public just accesses the merkle tree db directly.

How the executors were:

How they are after this pr:

I have altered the contexts for noir, both now have access to the roots

Checklist:

• I have reviewed my diff in github, line by line.
• Every change is related to the PR description.
• I have linked this pull request to the issue(s) that it resolves.
• There are no unexpected formatting changes, superfluous debug logs, or commented-out code.
• The branch has been merged or rebased against the head of its merge target.
• I'm happy for the PR to be merged at the reviewer's next convenience.

[LHerskind]

How should we handle duplicate leafs? The first one you know have not been spent? Just thinking with the idea proposed around also putting L1 to L2 in the commitments tree, would be a pity if you keep fetching the wrong index and cannot spend the note because there was two insertions with "deposit 10 eth to A".

[Maddiaa0]

My current idea is that if you have a transparent commitment then the nullifier's will need to be created with a different process. (Including the index) In the end to end test I was hoping to make a library that does this, but you are correct it does feel like a footgun.