Refactor auth providers to mutate request headers

[pakrym-oai]

Summary

• Move auth header construction into the AuthProvider::add_auth_headers contract.
• Inline CoreAuthProvider header mutation in its provider impl and remove the shared header-map helper.
• Update HTTP, websocket, file upload, sideband websocket, and test auth callsites to use the provider method.
• Add direct coverage for CoreAuthProvider auth header mutation.

Testing

• just fmt
• cargo test -p codex-api
• cargo test -p codex-core client::tests::auth_request_telemetry_context_tracks_attached_auth_and_retry_phase
• cargo test -p codex-core failed on unrelated/reproducible tools::handlers::multi_agents::tests::multi_agent_v2_followup_task_interrupts_busy_child_without_losing_message