MySQL 5.7 log rotate empty
Do you restart mysql daily?  That could explain the new logs.

Check these VARIABLES:

log_output = FILE   -- or TABLE,FILE
slow_query_log = ON
slow_query_log_file = /...   -- some valid path, including filename
long_query_time = 1   -- or some small value


Perhaps the general log hit a limit, thereby triggering an internal call to FLUSH LOGS, which rotated all logs?