Docs: add doctest for consistency

[moven0831]

Problem

• Documentation examples break when noir-rs APIs change, creating poor developer experience (see fix: correct import in readme #31). Examples aren't tested against actual code.

Solution

Implement doctests to automatically validate all documentation examples stay current with the codebase.

Acceptance Criteria

• Minimal working examples for all core noir-rs features, which should cover all modules in noir/src/backends/barretenberg/mod.rs
• Ensure examples are copy-pastable and self-contained
• Set up cargo test --doc in CI pipeline
• All code blocks in docs have doctest annotations
• All existing tests still pass
• All new doctests pass consistently

[moven0831]

@rubydusa are you interested in this issue as you suggested this in #31

[rubydusa]

I would be interested in this issue but I can't even build bb because of a glibc version mismatch - I'm on popOs 20.04 which has glibc2.35 but bb needs at least 2.38

I couldn't even run successfully the existing example after the import fix