Add CI testing for version compatibility between Nargo and NoirJS <> Barretenberg tooling
Problem Statement
There is currently no guarantee that new Barretenberg developments are compatible with Noir.
In other words, new Barretenberg developments could break Noir + Barretenberg users' works without us noticing firsthand.
Proposed Solution
Add Barretenberg bb and bb.js tests testing for compatibility with latest versions of Noir Nargo and NoirJS.
Noir currently has integration tests testing latest Noir's compatibility with a version of Barretenberg manually specified in https://github.com/noir-lang/noir/blob/master/scripts/install_bb.sh.
Translating those integration tests to test the other way round: latest Barretenberg against specific versions of Noir.
Additional Benefits
Tests would showcase best practices for how other proving backends should test compatibility with Noir.
@ledwards2225 is there a plan for detecting new Barretenberg changes that break compatibility with Noir in advance, ideally before PRs merge?