Refactor shared tracing queue to isolate tenant routing state

## Problem

The tracing pipeline uses a process-wide queue, while `TraceQueueManager` is request-scoped and carries `app_id`, `user_id`, provider, and Flask lifecycle state. The fix merged in #41403 preserves the originating `app_id` on each task, but the underlying design still couples a global work stream to stateful manager/timer instances.

This makes tenant routing correctness depend on mutable task state and leaves timer ownership, queue draining, and failure isolation difficult to reason about.