The easiest/simplest way to achieve your requirement, would be having your Entity Form as Edit mode, and set all fields (besides your status field) as read-only in the Dataverse form.. this way those fields wouldn't be updated when you submit the form
another thing to mention is that if the status field is the OOB Status Reason, I have the feeling you can't update that via Portals, you would need a workflow or Web API to update that
Another possible approaches for what you need:
Use classic Workflows and add them to your Entity Form, this would appear as a button in your form.. so basically you can have different buttons for "Mark record as XXX", and this would trigger the workflow which would update the record
Other option would be using Web API which is what I think what you are trying to do.. that would work but it seems too much work in my opinion
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