ci: run the root checks and tests through Turborepo

[userAugustos]

Goal

CI runs the same root commands a developer runs, through Turborepo, on every pull request and on main.

Acceptance Criteria

• CI installs Bun and uv at the pinned versions and runs bun install and uv sync.
• CI runs bun run check and bun run test from the root.
• CI uses Turborepo caching or filters so unchanged packages do not rerun.
• A failing test fails the workflow.

Guidance

• Stacked on the core test collection PR. Plan the details after that PR merges.