### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

No existing issue proposes the systematic fix, but several open issues are individual instances of the same failure class, where a field LiteLLM forwarded is rejected by a strict provider schema with "Extra inputs are not permitted": #23741 (vector_store_ids), #26240 (Claude Code), #27532 (context_management on /v1/messages passthrough), #23825 (tools[].custom.eager_input_streaming), #28081 (betas field on Converse). Each is being fixed one at a time; this issue proposes closing the class

### The Feature

Audit and harden provider request transforms so LiteLLM-internal `optional_params` keys can never be serialized into provider request bodies, with a single shared mechanism instead of per-handler `pop` calls.

Current state of the codebase:

There are 129 splat-style body constructions (`**optional_params` / `**inference_params` and similar) across `litellm/llms/`, for example `petals/completion/handler.py`, `openai_like/chat/handler.py`, `together_ai/completion/transformation.py`, `azure/azure.py`, `ovhcloud/embedding/transformation.py`. Each of these forwards …