feat: add Octane benchmark

[zhsama]

Summary

• Add a standalone Octane implementation of the Weather Front benchmark.
• Use Octane 0.1.34 with its official Vite plugin and compiled TSX components.
• Register Octane development, build, lint, test, documentation, and benchmark configuration.

Why

Octane compiles React-style components into direct DOM updates without a virtual DOM. This implementation makes its production output and source characteristics comparable with the other framework variants.

Impact

The existing framework implementations remain unchanged. Contributors can run the new app through the generated octane root commands.

Validation

• npm run build:octane
• npm run lint:octane
• npx playwright test --config=tests/config/playwright-octane.config.js --reporter=dot — 22 passed
• python scripts/verify/validate_schemas.py
• Source-analysis, bundle-size, and three-run build-time benchmark checks passed locally

[2u841r]

still draft?

[zhsama]

Sry, forgot to convert it from draft. Ready for review now.

[lissy93]

LGTM, thank you @zhsama

[lissy93]

Ah, the GitHub Actions workflows are failing which is why it's not live just yet.
But this isn't from this PR, seems that GitHub is just trying to keep to it's 20% downtime target 😅️

I'll come back in a couple hours and manually re-trigger them. I did test everything locally, so it should work 🤞️