docs(perplexity): document Agent API support (use_responses_api / useResponsesApi)

[James Liounis (jliounis)]

Summary

Documents Agent API support for ChatPerplexity in both Python and JavaScript, mirroring the use_responses_api / useResponsesApi flag pattern that ChatOpenAI already uses.

This is the docs counterpart to:

• Python: langchain-ai/langchain#37359 — feat(perplexity): add use_responses_api flag to ChatPerplexity
• JS: langchain-ai/langchainjs#10884 — feat(perplexity): add useResponsesApi flag to ChatPerplexity

Staged as draft until both code PRs land and the next langchain-perplexity (Python) and @langchain/perplexity (JS) releases ship. Once those packages publish, this PR is ready to mark ready-for-review.

What changed

Python — src/oss/python/integrations/chat/perplexity.mdx

Added an "Agent API support (use_responses_api)" section before "Using perplexity-specific parameters" with:

• Brief explainer on what the Agent API provides (richer tool-calling surface, native web search, structured web_search blocks).
• Comparison table: Search API (Chat Completions) vs Agent API (Responses).
• Code example: explicit use_responses_api=True.
• Code example: auto-detection via tools=[{"type": "web_search"}].
• Pointer to the Agent API model list.

JavaScript — src/oss/javascript/integrations/chat/perplexity.mdx

Added an "Agent API support (useResponsesApi)" section before "API reference" with TypeScript equivalents of the Python examples.

Provider pages

• src/oss/python/integrations/providers/perplexity.mdx — 1-line callout in the Chat models section linking to the new chat-page section.
• src/oss/javascript/integrations/providers/perplexity.mdx — same, for JS.

Conventions followed

• No references to deprecated sonar model branding — only sonar-pro (Search API) and Agent API model names where relevant.
• Mirrors the structure of the existing ChatOpenAI use_responses_api docs.
• Anchor IDs (#agent-api-support-use_responses_api, #agent-api-support-useresponsesapi) match the Mintlify slugification of the new section headers.

Why draft

Holding as draft so this lands together with (and not before) the SDK releases the flag. Once #37359 and #10884 are merged and the next langchain-perplexity / @langchain/perplexity versions are released, I will mark this ready and ping reviewers.

cc @langchain-ai/team

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🤖 Drafted with assistance from Perplexity Computer.