Ok, the standard way to do this is to edit the workflow. For each status where you want to prevent edit, add a workflow property that tells Jira to disallow editing (and commenting and other stuff you might want to block)
For a good example of this, go into the list of workflows and find the standard read-only default workflow, copy it and edit the copy, then take a look at the properties on the "closed" status.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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