### What happened?

When using github_copilot model provider via LiteLLM Proxy setup https://docs.litellm.ai/docs/providers/github_copilot#usage---litellm-proxy

During long-running multi-turn agentic processes (ex. Plan mode, triggering subagent flows and tool calls, implementation of TODO list, etc.) only 1 GitHub Copilot premium request should be used, at the time of initial user-initiated message prompt docs: https://docs.github.com/en/copilot/concepts/billing/copilot-requests

the premium request usage expected behavior can be observed using vscode copilot chat Agent or Plan modes, github copilot CLI, as well as successfully implemented in other open-source repos such as from OpenCode https://github.com/sst/opencode-copilot-auth/blob/main/index.mjs and CopilotApi Proxy https://github.com/ericc-ch/copilot-api/blob/master/src/services/copilot/create-chat-completions.ts

I am not sure how these implementation differ entirely since all (including LiteLLM) do similarly consider mapping of "X-Initiator" header https://github.com/BerriAI/litellm/blob/main/litellm/llms/github_copilot/chat/transformation.py https://github.com/BerriAI/litellm/blob/main/litellm/llms/github_copilot/respon…