test: fix flakiness in gh_6128_background_mode_test
Test runs an external process with tarantool that writes to a log file. Then test reads that log file and searches a string with required message in it (see function check_err_msg). Test was flaky on macOS and I suspect it was happening due to a high log level - timeout was not enough to wait message in the log file. Patch decreases a log level to a default value and replaces io functions with the similar alternatives in a fio module. Using fio functions allows to not block fibers. NO_CHANGELOG=test fix NO_DOC=test fix