Add option to write log output to a timestamped log file.

### Context
We may want to preserve and/or share the outputs of running the various python scripts. Let's provide a consistent option to do so.
### Thoughts

- I'd suggest we auto-generate the filename and write it to the `./logs` folder.
- For now I hope we can rely and reuse the code we've got to detect the root of the repo to locate the {repo_root}./logs folder. This won't work as-is if we release this code e.g. as a pip package.
- How about adding a `--preserve-log` command-line option to all the currently active scripts in `./src` and `./utils`?

Start by reviewing the currently active Python scripts in ./src and ./utils, along with the existing code that detects the repository root and handles log output. Trace how each script parses command-line options and where output is written. Done means --preserve-log is consistently available, generates a timestamped filename under ./logs, and preserves the script output.

Written by the indexing model from the issue text.