fix: de-duplicate public inputs in BB proofs

[guipublic]

Description

Problem*

Resolves #4443

Summary*

Barretenberg append public inputs to the proof, which are removed in Noir and prepended again before verification.
However in Noir duplicate witnesses are removed, although not in Barretenberg, which generates a discrepancy.

Additional Context

Documentation*

Check one:

• No documentation needed.
• Documentation included in this PR.
• [For Experimental Features] Documentation to be submitted in a separate PR.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[TomAFrench]

I'm gonna close this PR as it should be moot after #4951.