test: broken_sstable_test: prepare for asynchronously closed sstables_manager
test: broken_sstable_test: prepare for asynchronously closed sstables_manager

Instead of using an asynchronously-constructed and destroyed
test_env, obtain one using test_env::do_with(), which is
prepared for async close.

scylladb/scylla,scylladb/scylla,scylladb/scylla,scylladb/scylla