fix: exclude undefined cost from providerMetadata

[robert-j-y]

Description

Fixes #262 - When models like gemini-3-pro-preview don't return a cost value, the providerMetadata object was including cost: undefined. Since undefined is not a valid JSON value, this caused AI SDK validation failures when passing providerMetadata back into subsequent conversation turns.

Before:

providerMetadata: {
  openrouter: {
    usage: {
      promptTokens: 17,
      completionTokens: 227,
      totalTokens: 244,
      cost: undefined,  // ❌ Invalid JSON value
    }
  }
}

After:

providerMetadata: {
  openrouter: {
    provider: 'openai',  // Now included for consistency
    usage: {
      promptTokens: 17,
      completionTokens: 227,
      totalTokens: 244,
      // cost field omitted when undefined ✓
    }
  }
}

The fix uses conditional spreading/assignment to only include cost when it has a defined value, matching the existing pattern used for other optional fields like costDetails.

Changes Summary

• Chat model: Conditional spreading for cost in both doGenerate and doStream
• Completion model:
  • Added providerMetadata with schema validation in doGenerate (was missing entirely)
  • Added provider field tracking in doStream
  • Added provider field to completion schema
• Embedding model:
  • Now always returns providerMetadata with full usage structure and schema validation via OpenRouterProviderMetadataSchema.parse()
  • Added provider field to schema

Updates since last revision

• Added comprehensive test coverage for completion model's doGenerate providerMetadata:
  • should return providerMetadata with usage and provider - verifies basic structure
  • should omit cost from providerMetadata when undefined - verifies the main bug fix
  • should include cost: 0 in providerMetadata when cost is zero - verifies zero cost is preserved
  • should default provider to empty string when not returned by API - verifies fallback behavior
  • should include token details in providerMetadata when provided - verifies full feature coverage

Human Review Checklist

• Verify cost: 0 is still correctly included (the != null check allows this)
• Confirm all affected locations were fixed:
  • src/chat/index.ts - doGenerate (line ~485) and doStream (line ~703)
  • src/completion/index.ts - doGenerate (line ~224, uses schema validation) and doStream (line ~419, tracks provider)
  • src/embedding/index.ts - doEmbed (line ~93, uses schema validation)
• Verify the behavioral changes are acceptable:
  • Embedding model now always returns providerMetadata with full structure (previously undefined when no cost)
  • Completion model doGenerate now returns providerMetadata with schema validation (previously didn't return it at all)
  • All models now include provider field (defaults to '' when not returned by API)
• Note: doStream methods build metadata manually without schema validation (matches existing chat model pattern for streaming performance)

---

Link to Devin run: https://app.devin.ai/sessions/7543a73deec84146abe08abf555d19a9
Requested by: Robert Yeakel (@robert-j-y)

Checklist

• I have run pnpm stylecheck and pnpm typecheck
• I have run pnpm test and all tests pass
• I have added tests for my changes (if applicable)
• I have updated documentation (if applicable)

Changeset

• I have run pnpm changeset to create a changeset file