Production-candidate STM library for IVC SNARK

## Why

The MVP of the recursive SNARK proofs (#2529) delivered a working IVC implementation in the `mithril-stm` library, but it is not production ready: the circuits are still partly coupled to the underlying proving library, some off-circuit checks are missing, the recursive and non-recursive implementations have diverged, the testing strategy is slow and incomplete, and the documentation does not cover the recursive scheme.

## What

Bring the IVC SNARK implementation of the `mithril-stm` library to a production-candidate state: harden and optimize the circuits and the proving pipeline, complete the missing verification checks, harmonize the recursive and non-recursive implementations, make the library usable by default, and deliver the testing strategy and the documentation which back it.

## TBD
- [ ] https://github.com/orgs/IntersectMBO/projects/78/views/3?pane=issue&itemId=215823287
- [ ] https://github.com/orgs/IntersectMBO/projects/78/views/1?pane=issue&itemId=215823290
- [ ] https://github.com/orgs/IntersectMBO/projects/78/views/1?pane=issue&itemId=215823298
- [ ] https://github.com/orgs/IntersectMBO/projects/78/views/1?pane=issue&itemId=218915954
- [ ] https://github.com/orgs/IntersectMBO/projects/78/views/5?pane=issue&itemId=222533269

Start by reviewing the mithril-stm library and the MVP context in issue #2529, then follow the five linked project work items. The issue names no files, entry points, or tests, so the scope must be mapped before work begins. Done means the circuits and proving pipeline are hardened, checks and implementations are aligned, testing is complete, and recursive-scheme documentation is delivered.

Written by the indexing model from the issue text.