docs: document provider reasoning request formats

[rekram1-node]

Summary

• document raw HTTP formats for reasoning toggles, effort levels, and token budgets across the selected provider SDKs
• distinguish provider-wide request shapes from model-, route-, region-, and endpoint-specific behavior
• cite primary provider documentation, schemas, live metadata, or first-party source inline in each relevant TOML
• explicitly record when a provider does not document a reasoning control instead of inferring upstream behavior

Scope

This covers 131 provider scopes using the selected SDKs, including provider-level and model-level @ai-sdk/openai-compatible overrides. All changes are TOML comments only; model metadata and reasoning_options are unchanged.

Validation

• bun validate
• git diff --check
• comment-only integrity check against HEAD