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Per your description, It seems that you want to restrict the issues from to be assigned, allowing the users to change its assignee ONLY after the issue has been transitioned through all the triage statuses in your workflow. Is that correct?
If that's what you are looking for, you can use the "jira.permission.assign.projectrole" priority to properly avoid your issue to be assigned. That would be the steps:
1 - Logged as the site-admin, create a project role that is not added with any users. Once you create it, click to edit the new project role and check in the browser URL which is the respective ID:
2 Navigate to your project > Project Settings > Workflows > Edit > For all the status and transitions you want to block the issue from being assigned, add the following property, where the projectroleID is the ID you checked when created the project role:
the jira.permission.assign.projectrole = projectroleID
3 - Save your workflow draft
Let us know if this is the option you are looking for.
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