No CI job exercises pixi.toml, so the development environment can rot silently

[IvanaGyro]

Problem

pixi.toml and pixi.lock describe the development environment contributors are pointed at from CONTRIBUTING.md, but nothing in CI touches them. ci-cmake_tests.yml installs its dependencies with apt and mamba and calls cmake directly, so every CI check can be green while:

• a task is broken or renamed,
• the lock no longer solves for a platform,
• the lock has drifted from the manifest (pixi lock --check would fail),
• a dependency needed to configure has been dropped.

A contributor finds out instead of a check.

Suggestion

A small workflow on ubuntu-latest:

- run: pixi lock --check     # manifest and lock agree
- run: pixi install
- run: pixi run test-cpp     # configure, build test_main, run the C++ suite

pixi run test-cpp covers setup and configure through its dependency chain, so a broken task in the middle fails the job. pixi lock --check is nearly free and catches the drift case on its own — worth running even if the build half is judged too expensive for every PR.

Two details that would decide the shape:

• detached-environments. cytnx exports its LAPACKE include directory as a PUBLIC usage requirement, so with Pixi's default in-checkout layout CMake refuses to generate (INTERFACE_INCLUDE_DIRECTORIES ... which is prefixed in the source directory). The job needs pixi config set --local detached-environments true, the same step CONTRIBUTING.md documents, until Fix exported CMake usage requirements and relocatable dependencies #1120 removes the need.
• Which preset. pixi run test-cpp defaults to openblas-cpu, matching the PyPI wheel. pixi run gate covers both debug-* CPU presets but roughly triples the runtime.

Caching the Pixi environment between runs would keep the cost down; the lock file is a natural cache key.

Context

Raised while reworking the Pixi setup so the preset is a task argument and one environment serves every preset. Deliberately left out of that PR to keep the diff scoped to the development environment rather than CI.