Manually deleting log files breaks the file purge (expiration).

Heading was: Harden BLR binlog file-index handlin

Manually deleting log files breaks the file purge (expiration). It is likely that an unfortunate crash could leave the index invalid as well.
Make the index file "for human information only". Re-read log file names and update times, and recreate the index file every time the index file is currently consulted.