[codex] Restore Carbon ads fallback

[brandonkachen]

Summary

• Move ads fallback ordering to the server so a Gravity request falls through to ZeroClick and then Carbon.
• Remove the CLI-side fallback loop so clients make one ads request and trust the server-selected provider.
• Add endpoint coverage for Gravity -> ZeroClick -> Carbon fallback and for skipping an unconfigured ZeroClick provider while still reaching Carbon.

Why

Carbon had previously been used as a backup provider, but the current client-side fallback path only tried Gravity and ZeroClick. Keeping the fallback chain on the server gives us one place to control provider ordering and makes Carbon available as the third backup without another client request loop.

Validation

• bun test web/src/app/api/v1/ads/__tests__/ads.test.ts web/src/lib/ad-providers/__tests__/carbon.test.ts web/src/lib/ad-providers/__tests__/zeroclick.test.ts
• bun run --cwd web typecheck
• bun run --cwd cli typecheck
• git diff --check