Document the Gateway provider lifecycle API

[ddanielcruzz]

Context

pydantic/platform#26950 adds the organization-owned Gateway provider lifecycle under /v1/gateway/providers/. Its walkthrough references docs/reference/api/gateway-providers.md, but that page does not exist yet.

This documentation should land before the endpoint is announced or released.

Scope

• Document authentication and the required organization:read and organization:write scopes.
• Cover create, list, read, update, credential rotation, and delete requests.
• Explain newest-first keyset pagination and cursor handling.
• Document plan gating and the structured 402 response.
• Document 404, 409, and 422 behavior.
• Make credential redaction guarantees explicit.
• Include request and response examples and link to the runnable platform walkthrough.

Done when

• docs/reference/api/gateway-providers.md exists and is linked from the appropriate API reference navigation.
• Examples match the contract in pydantic/platform#26950.
• The platform walkthrough link resolves to this page.
• The documentation is merged before the endpoint is announced.