fix: shorebird cache clean fails with log file not found

[erickzanardo]

Description

When trying to run shorebird cache clean we get the following error:

✗ Failed to delete cache directory /Users/erick/projects/shorebird/shorebird/bin/cache: FileSystemException: Deletion failed, path = '/Users/erick/Library/Application Support/shorebird/logs' (OS Error: Directory not empty, errno = 66) (0.8s)

This is mostly likely happening because we delete the log file in this command, but tries to log to it to show the completed progress.

Also reported at #2231

Steps To Reproduce

1. run shorebird cache clean
2. see erro

Expected Behavior

shorebird cache clean should no fail with error