Export logs to a file with `--log` option.

Currently, we can get the report with `--report` flag, but lack a export of log to a output file.

### Task List:

- Add a `--log` flag. This flag will be optional.
- If a flag is provided, create a log file inside the output directory.

Start by locating the CLI argument parsing and the existing --report output handling, then run the command's help or current tests to understand the output directory behavior. Done means --log is optional and, when provided, creates a log file inside the output directory without changing the existing report behavior.

Written by the indexing model from the issue text.