[codex] render official AI directory logos

[trsoliu]

Summary

This PR replaces AI directory letter placeholders and incomplete logo coverage with local official logo assets for every current directory entry.

What changed

• Added a generated logo map for all 213 AI directory entries and aligned the existing JSON logo map with it.
• Added local logo assets under static/img/ai-directory/logos/, including the missing Qoder, Trae, Kiro, and Qoder CLI cards.
• Updated the AI directory catalog contract to require a local logo path for each entry.
• Added npm run sync:ai-directory-logos plus a Node test that verifies every entry has a declared, existing, renderable image asset.
• Kept the latest AiDirectoryGrid implementation and made it prefer the validated per-entry logo path.

Validation

• npm run sync:ai-directory-logos
• npm run test:teaching-videos
• npm run build
• Local static preview confirmed Qoder, Trae, Kiro, and Qoder CLI render image URLs under /website/img/ai-directory/logos/.

Notes

npm run build still emits the existing webpack warning from vscode-languageserver-types; the build exits successfully.