bind_task_tool and _bind_batch_tool copied their process-wide singletons
with only the coroutine rebound. Once get_available_tools had wrapped a
singleton in place with a sync func, the copy inherited that wrapper
around the unbound coroutine, so synchronous invocation bypassed the
explicit SDK submitter/capacity and fell through to the process-global
one -- or raised NotImplementedError in a fresh process where the
singleton was never wrapped.
Rebind the copy's func to a sync wrapper around the bound coroutine so
both invocation paths use the runtime's own submitter and capacity.
5242fcfb63