## Problem

LiteLLM emits structured JSON log records via three module-level logger singletons (`verbose_logger`, `verbose_proxy_logger`, `verbose_router_logger`) instantiated in `litellm/_logging.py`. `JsonFormatter.format()` (lines 159-190) serializes `message`, `level`, `timestamp`, extra `{}` kwargs, and embedded Python dicts but has no mechanism to inject request-scoped identifiers such as `session_id` or `trace_id` into the emitted JSON record.

In production environments with concurrent async requests, this means log lines are interleaved with no way to group them per request. The `Logging` object created per-request in `litellm/litellm_core_utils/litellm_logging.py` does hold `self.litellm_trace_id` (line 347), but that object is never accessible from inside `JsonFormatter.format()`. Operators cannot reconstruct a request's lifecycle from logs alone.

## Root cause

`JsonFormatter` in `litellm/_logging.py` has no request-scoped context. The `Logging` object's `litellm_trace_id` and caller-supplied `litellm_session_id` are never stored in a `ContextVar`, so they cannot be read inside `format()` without passing them through every intervening function call.

## Reproduction

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