feat(jax): implement profiler lifecycle and trace output #5871

Summary

The JAX trainer reads training.profiling and training.enable_profiler, but there is no complete profiler lifecycle or trace-export path in the training loop.

Scope

• Define the intended semantics of both schema options for JAX.
• Start profiling at the configured lifecycle point, advance it with completed training steps, and stop it on normal or exceptional exit.
• Honor the configured trace/output path.
• Prevent output collisions between distributed ranks.
• Keep profiler control outside compiled/jitted train-step functions.
• Make the disabled path a true no-op.

Acceptance criteria

• Each profiling option works independently and in combination according to documented semantics.
• A valid trace is produced at the configured path.
• Resources are finalized after both successful training and controlled failure.
• Distributed output names are deterministic and collision-free.
• Tests verify lifecycle ordering, disabled behavior, and trace creation without changing numerical training results.

Refs #5756.

Coding agent: Codex
Codex version: codex-cli 0.144.4
Model: gpt-5.6-sol
Reasoning effort: xhigh