refactor(acvm_js): Improve program handling and error messages in wit…

[VolodymyrBg]

…ness extraction

Problem

Resolves #4428

Summary

This PR improves the handling of ACIR programs in the ACVM JS bindings witness extraction functions by:
Updating documentation to correctly refer to "program" instead of "circuit"
Improving error handling for multi-circuit programs
Making error messages more descriptive and consistent
Restructuring program validation logic for better maintainability
Preparing codebase for future multi-circuit support while maintaining current functionality

Additional Context

The changes maintain compatibility with the current single-circuit limitation of the native ACVM executor while making the code more maintainable and future-proof. The error messages have been improved to be more helpful for developers.

Documentation

[x] No documentation needed.
PR Checklist
[x] I have tested the changes locally.
[x] I have formatted the changes with cargo fmt on default settings.

[github-actions]

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