Add recursive proof Solidity tests

[Savio-Sou]

Context

Now that basic Solidity verifier tests have been reintroduced with #2997, it would be great to expand the tests to cover more barretenberg features exposed through Noir to better guarantee they work end-to-end from a Noir app dev perspective.

Separately, we currently do have a recursive test(?) but that doesn't seem to capture the failing workflow below.

Problem

Similar to #3048, I would suggest prioritizing also the testing of recursive proof given issues reported with the particular function:

• On-chain verification fails for recursive proofs noir-lang/noir#3166
• Slack debugging thread

The failing workflow goes by:

1. We generated an inner proof with bb
2. We then generated a final proof which verified the inner proof with bb
3. We then tried to verify that outer proof with the solidity verifier contract

Extending our current tests to cover the failing workflow asap should help provide further insights on how to debug the existing issues.

Objectives

(Open to discussion as I am in lack of barretenberg's technical context to judge if these make sense.)

Extend tests to cover:

1. Generate an inner proof as a part of recursion
2. Generate a final proof that verifies the inner proof
3. Verify the final proof natively
4. Generate a corresponding Solidity verifier
5. Verify the final proof via the Solidity verifier

Using:

1. Native barretenberg
2. bb binary
3. bb.js

[Maddiaa0]

closed by #3161