fix: displaying stdout/stderr with errors-only (#6446)
### Description
This PR fixes up our `errors-only` behavior by making sure we flush the
file writer by the time we attempt to replay the logs.
### Testing Instructions
`run-logging/errors-only.t` and `run/continue.t` now both pass
Closes TURBO-1663
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Co-authored-by: Chris Olszewski <Chris Olszewski>
