Fix reasoning not working for MiniMax Coding Plan

[chrarnoldus]

Seems to be a Vercel bug: reasoning does not show when using chat completions

Partial fix for: Kilo-Org/kilocode#11334

[kilo-code-bot]

Code Review Summary

Status: No Issues Found | Recommendation: Merge

Executive Summary

Adds targeted MiniMax reasoning fixes — disables default thinking in the Messages API to match Anthropic SDK behavior, and routes MiniMax through the Anthropic provider on Vercel AI Gateway so reasoning surfaces correctly. Both changes are minimal, follow existing patterns, and are well-documented with inline references.

Files Reviewed (2 files)

• apps/web/src/lib/ai-gateway/providers/apply-provider-specific-logic.ts
• apps/web/src/lib/ai-gateway/providers/model-settings.ts

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_{Reviewed by deepseek-v4-pro-20260423 · 262,390 tokens}

_{Review guidance: REVIEW.md from base branch main}