feat(tools): add Perplexity Search

[esafwan]

Consolidated scope

Extracts the Perplexity Search feature from the combined search implementation.

Original PR

• feat: add Google Search and Perplexity Search agent tool types #439: originally contained both Google Search and Perplexity Search; this PR contains only Perplexity Search

Included functionality

• Perplexity Search tool type
• Agent tool schema and validation
• App seeding and flow execution registration
• Frontend tool template and type registration
• LiteLLM perplexity/sonar execution
• Site-configured or environment-provided Perplexity credentials
• Answer and citation response normalization

Google Search is tracked separately in #462. Targets integration/huf-consolidation-2026-07; included in final integration PR #468.