I saw such a command in some code examples (it is used to save the progress of data replication)

meltano elt tap-rest-api target-jsonl --job_id=earthquakes

When I ran it myself, I got an error Error: No such option: --job_id Is there a replacement for this item? It seems I need the --state-id argument. I'm right?

Yes, --job-id is replaced with --state-id