[CI/Build] Fix local CI guidance

[Hubert-Zhu]

Description

The built-in local CI skill, README, plugin manifest, and pull request template
referenced scripts/run_ci_test.sh, but that entry point does not exist on
main.

This change:

• replaces the broken single-runner guidance with existing repository commands;
• documents targeted pre-commit, formatting, C++, TENT, and wheel checks;
• clarifies that macOS is suitable for lightweight checks while Linux is needed
  for build and service-based validation; and
• keeps GitHub Actions as the authoritative full validation environment.

No production code or GitHub Actions workflow behavior changes.

Open PR overlap check

• [Weight] Add runtime weight manifest contracts #3187 also touches the PR template to add an unrelated module entry.
• [Doc] Add Mermaid diagram and support status table to README #2711 also touches README architecture and ecosystem content.

Neither changes the local-CI skill or the stale run_ci_test.sh references;
any merge conflict should be limited to separate lines.

Module

• CI/CD
• Docs
• Other

Type of Change

• Bug fix
• New feature
• Refactor
• Breaking change
• Documentation update
• Performance improvement
• Other

How Has This Been Tested?

Test commands:

python3 -m json.tool .claude/skills/mooncake-ci-local/.claude-plugin/plugin.json
git diff --check origin/main...HEAD
if rg -n "run_ci_test\\.sh" README.md .claude .github; then exit 1; fi
pre-commit run --from-ref origin/main --to-ref HEAD

Test results:

• Targeted pre-commit hooks pass
• Plugin manifest parses as JSON
• No references to the missing runner remain
• Manual review confirms replacement commands and paths exist

Checklist

• I have performed a self-review of the change
• I have formatted code using ./scripts/code_format.sh (not applicable; no code changed)
• I have run pre-commit run --all-files (targeted branch-diff hooks were run)
• I have updated the documentation
• I have added tests (not applicable; guidance-only change)
• For changes >500 LOC: I have filed an RFC issue (not applicable)

AI Assistance Disclosure

• No AI tools were used
• AI tools were used

Codex identified the stale references, updated the contributor guidance, and
ran targeted validation. The human submitter remains responsible for reviewing
and defending the change.