docs: Provider reasoning capability probing matrix and documentation

[Oaklight]

Context

We have accumulated significant probing data across multiple providers and API formats for reasoning effort support, thinking type behavior, and disabled strategies. This data is currently scattered across multiple issues and comments. We need a consolidated arching issue to track all probing work and ultimately produce a documentation page.

Goal

Create a comprehensive documentation page (in both docs_en and docs_zh) covering:

1. Per-provider reasoning effort support matrix — which effort values each provider/endpoint accepts or rejects
2. Disabled behavior — how each provider handles none / disabled reasoning (omit vs thinking_disabled vs specific field values)
3. Thinking type — enabled vs adaptive behavior per provider, model-level overrides
4. Provider metadata round-trip — reasoning_details, encrypted_content, thoughtSignature preservation
5. Shim configuration reference — how ReasoningCapability fields map to upstream behavior

Existing probing data

Argo parameter probing

• Comprehensive per-model ARGO parameter probe for shim capability tables #220 — Comprehensive per-model ARGO parameter probe
  • Full probe results (2026-05-23)
  • Progress update (2026-06-09)

Reasoning effort probing (official upstream APIs)

• Normalize reasoning/thinking fields across OpenAI Chat-compatible providers via shim transforms #185 comment — Reasoning effort probing results (2026-06-10)
  • Covers: OpenAI, Anthropic (via OpenRouter), DeepSeek, Volcengine, MiniMax (both endpoints)
  • Effort value acceptance matrix, disabled behavior verification

Reasoning effort IR design

• PR fix: accept reasoning.effort "none" and "xhigh" in Responses endpoint (#244) #245 — reasoning.effort "none" and "xhigh" handling in Responses endpoint
• PR feat: multi-API shims for MiniMax/Volcengine + reasoning metadata round-trip (#185, #186) #266 — reasoning metadata round-trip + Volcengine/DeepSeek effort map updates based on probing

Thinking type normalization

• Argo thinking type normalization incomplete and misplaced #254 / feat: model-level thinking_type in shim reasoning config (#254) #256 — thinking_type field in ReasoningCapability, model-level overrides via model_reasoning

Sub-tasks

• Consolidate all probing results into a single reference table
• Document per-provider shim configuration and rationale
• Write docs_en/docs/guide/provider-reasoning.md
• Write docs_zh/docs/guide/provider-reasoning.md
• Update mkdocs.yml nav in both doc worktrees
• Cross-reference from existing reasoning guide page

Related issues

• Normalize reasoning/thinking fields across OpenAI Chat-compatible providers via shim transforms #185 — Normalize reasoning/thinking fields across providers
• Comprehensive per-model ARGO parameter probe for shim capability tables #220 — Comprehensive per-model ARGO parameter probe
• feat: restore ModelShim for per-model transforms #192 — ModelShim for per-model transforms
• Define gateway proxy/conversion boundaries and stream conversion modes #248 — Gateway proxy/conversion boundaries