docs: add missing integration guides (streaming, tool-calling, anthropic-messages, embeddings, responses, audio, images, rerank, passthrough, errors-and-retries)

Background

Follow-up to #246 (closed by #249). The docs rebuild shipped one of the eleven planned integration pages at full quality, plus a baseline errors-and-retries.md:

• ✅ docs/integration/openai-compatible-api.md — full request-flow mermaid + endpoint surface + auth
• ✅ docs/integration/errors-and-retries.md — status-code table, error.type strings verified against ProxyError

The other ten pages exist but are placeholder-tier and need expansion. Per #240's "Remaining Work Breakdown", they are tracked here as separate doc refinements.

Scope

Expand each page to match the depth of openai-compatible-api.md (request shape, response shape, streaming behavior where applicable, provider compatibility, real curl + SDK example, anchor to the corresponding e2e test):

• docs/integration/streaming.md — SSE event ordering, abort behavior, partial-chunk semantics
• docs/integration/tool-calling.md — cross-provider tool-use translation; anchor to tests/e2e/src/cases/tools-cross-provider-e2e.test.ts
• docs/integration/anthropic-messages.md — full /v1/messages reference; OpenAI → Anthropic translation matrix
• docs/integration/embeddings.md — providers that implement it, dimension handling
• docs/integration/responses.md — OpenAI Responses API surface; current OpenAI-provider-only constraint
• docs/integration/audio.md — transcriptions / translations / speech; per-provider compatibility
• docs/integration/images.md — /v1/images/generations; provider compatibility
• docs/integration/rerank.md — Jina AI rerank surface (per #229)
• docs/integration/passthrough.md — /passthrough/:provider/*rest semantics, auth boundary

Acceptance criteria

For each page:

• request body shape with every field documented in a table (type / required / description)
• response body shape with every observable field
• error envelope behavior for endpoint-specific failure modes
• at least one runnable curl example + at least one SDK example where the SDK supports the endpoint
• citation of the e2e test that pins the contract

References

• Parent rebuild PR: #249
• Original integration-guides issue: #246

Start by comparing the placeholder pages in docs/integration/ with docs/integration/openai-compatible-api.md and review the linked e2e cases, especially tests/e2e/src/cases/tools-cross-provider-e2e.test.ts. Expand the ten listed guides with the specified request, response, error, compatibility, curl, SDK, and e2e-contract details. Done means every acceptance criterion is covered for each page.