feat(search): Perplexity Search API connector as alternative to anthropic_web

[bjridicodes]

Context

The current `anthropic_web` fallback connector uses Claude to browse and extract job listings, which is expensive in tokens and prone to returning stale or hallucinated URLs. Perplexity's Search API returns real, indexed URLs with titles and snippets at a flat rate — no LLM overhead on the discovery step.

Idea

Implement a `perplexity` search connector that calls the Perplexity Search API for job discovery, slotting into the existing provider layer.

Why it's interesting

• Eliminates hallucinated/fabricated URLs (Perplexity only returns indexed results)
• Decouples discovery (Perplexity, cheap) from analysis (Claude, controlled)
• Real-time index with source citations usable as the `url` field in job records
• Could serve as a first-class connector, not just a fallback

Pricing reality (assessed 2026-05-14)

• Search API: $5 per 1,000 requests (flat, no token cost)
• At ~13 queries/run → ~$0.065/run → ~77 runs per $5
• Cost is real and ongoing — not a pure token substitution, it's additive unless it fully replaces `anthropic_web`
• Decision: defer to Phase 6 until token cost baseline is established and net savings are measurable

Open questions

• Does Perplexity's index cover French job boards well (Welcome to the Jungle, APEC, Cadremploi, company career pages)?
• Result quality vs. `anthropic_web` for senior PM roles in Paris — untested
• Integration path: new `PerplexitySearchProvider` following the existing connector pattern

Out of scope for this issue

• Perplexity Sonar (LLM) models — different pricing tier, different use case
• Replacing France Travail / Adzuna (those are opt-in for other user profiles)

Related

• Closes the idea filed in `wiki/projects/ajsaa/ideas/unimplemented/perplexity_mcp_websearch.md`
• Related to fix(search): LLM web search returns stale/404 jobs, recency filter not enforced #19 (stale/404 job fix — URL validation remains necessary regardless of provider)