Fetching stage outputs progress into log

### Checklist

- [x] I added a descriptive title
- [x] I searched open reports and couldn't find a duplicate

### What happened?

Fetching outputs progress into the log. This can make logs very difficult to read, especially for large installers.

Example run: https://github.com/conda/constructor/actions/runs/12017768460

### Additional Context

_No response_

Start by reviewing the example GitHub Actions run to reproduce how fetching stage outputs appears in the log, then trace that output to the relevant logging entry point. Done means progress from fetching outputs no longer makes logs difficult to read for large installers.

Written by the indexing model from the issue text.