feat(llm): add Perplexity as a model provider

[jliounis]

Motivation

Continue's provider list covers 25+ inference services but Perplexity is missing. Perplexity's Sonar family (sonar, sonar-pro, sonar-reasoning, sonar-reasoning-pro) ships with built-in web search, which is particularly relevant for coding agents that need to research up-to-date documentation or APIs while answering — a common workflow in Continue.

The Perplexity API is OpenAI-compatible, so this PR mirrors the pattern used by other OpenAI-compatible providers like Groq, Together, OpenRouter, and Inception: the provider class subclasses OpenAI and only overrides providerName and apiBase. No custom request/response transformation is needed.

Changes

• core/llm/llms/Perplexity.ts — provider class extending OpenAI with apiBase = "https://api.perplexity.ai/" and default model: "sonar"
• core/llm/llms/index.ts — registered in LLMClasses (import + array entry)
• core/llm/autodetect.ts — added "perplexity" to the list of providers that use OpenAI templating
• packages/openai-adapters/src/types.ts — added "perplexity" to the OpenAIConfigSchema union
• packages/openai-adapters/src/index.ts — added the case "perplexity" factory branch
• extensions/vscode/config_schema.json — added "perplexity" to the provider enum, the model if/then block (Sonar models + AUTODETECT), and a markdown description
• docs/customize/model-providers/more/perplexity.mdx — new provider page modeled on groq.mdx
• docs/customize/model-providers/overview.mdx — added to the hosted-services table
• docs/docs.json — added to the More providers sidebar group
• core/llm/llms/Perplexity.vitest.ts — tests via the existing createOpenAISubclassTests helper

Tests

core/llm/llms/Perplexity.vitest.ts calls createOpenAISubclassTests(Perplexity, ...), the same helper used by Groq, Together, and other OpenAI-compatible providers. The helper generates 7 cases covering: providerName, default API base, streamChat, chat, streamComplete, complete, and embed against a mocked fetch. Run with:

```
cd core && npm run vitest -- llms/Perplexity
```

References

• Perplexity API getting started: https://docs.perplexity.ai/docs/getting-started
• Mirrored pattern: `core/llm/llms/Groq.ts`, `core/llm/llms/Together.ts`

---

Summary by cubic

Adds Perplexity as a first-class LLM provider using its OpenAI-compatible API, with default sonar model. This enables Sonar models (sonar, sonar-pro, sonar-reasoning, sonar-reasoning-pro) with built-in web search for fresher answers.

• New Features
  • Added Perplexity provider extending OpenAI with apiBase: "https://api.perplexity.ai/" and default model: "sonar".
  • Registered in LLMClasses and added to OpenAI-templated autodetect providers.
  • Updated packages/openai-adapters types and factory to support perplexity.
  • Updated VS Code config_schema.json with provider enum, Sonar model list (AUTODETECT supported), and help text.
  • Added docs: provider page, overview entry, and sidebar link.
  • Added unit tests via createOpenAISubclassTests for core chat/complete/embed paths.

^{Written for commit f4bdacd. Summary will update on new commits. Review in cubic}

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[cubic-dev-ai]

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[jliounis]

I have read the CLA Document and I hereby sign the CLA

I have read the CLA Document and I hereby sign the CLA

[jliounis]

I have read the CLA Document and I hereby sign the CLA