Background review fork redirected stdout/stderr around run_conversation()
so its iteration messages stay silent.  But the memory-provider teardown
(shutdown_memory_provider() and review_agent.close()) fired in the outer
finally block AFTER the redirect_stdout context exited — so provider
teardown prints (Honcho disconnect, Hindsight sync, etc.) leaked into
the parent terminal at end of every turn.

Moves the teardown inside the redirect_stdout scope on the success path
(and nulls review_agent so the finally safety-net skips double-shutdown).
The finally block is rewritten as an exception-path safety net that
re-opens a devnull redirect, since the original 'with' context has
already exited by the time finally runs.

Salvage of #25342 by @ayushere (manually re-applied + merged conflict
with current main's set_thread_tool_whitelist wiring).