The question to publish a workflow only shows if it is active (in use by at least one project). The draft-system of workflows is to make sure no projects are interfered by workflow changes (until they are done).
Your newly created workflows should hide under "Inactive" until they are being used.
When you click your workflow scheme, dont you get a button to "Add Workflow" in the top right corner of the screen? There is where you associate a workflow with an issue type and make it associated to your workflow scheme.
Hope this helps, if not please elaborate about your issue!
Unfortunately the Next-Gen projects don't have the feature to edit workflows, since it is supposed to be an out-of-the-box setup needing only minor configurations. Atlassian has an active ticket about implementing this functionality.
If you would consider a classic jira project, then this tutorial about editing workflows might come in handy!
Hope this helps!
Good luck with your Jira endeavours!
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