Ship DBT logs to consumer task in WATCHER_KUBERNETES mode

[pankajastro]

Previous PRs #2412 and #2431 improved consumer task logging in WATCHER mode by shipping startup and error logs to the consumer.

This PR extends that functionality to WATCHER_KUBERNETES mode, including testing and implementation to ensure the same logs are properly shipped.

[github-actions]

This issue is stale because it has been open for 30 days with no activity.