In the job script itself, you are creating such files, so some of the proposed use cases are a bit tricky to get right in the way you described them. For example, if you scp these files, you are scp'ing them to their status before scp is run. Something else might happen (e.g. scp warnings) which will be added to the files after the command is run, and those would not be included. Also, the buffers might not have flushed, so the scp'ed version can be incomplete. Even worse for post-processing, which can be covered better with something like the following in the slurm script

program_that_creates_lots_of_output | tee full_output_just_in_case_is_needed.txt | post_processing_script

So that the original slurm file will automatically contain the post-processing version, and the "just in case" file will contain the full log. Of course the name of the latter does not need to be hardcoded and can use things like $SLURM_JOB_ID to make it unique for each job.