I've got the edit privilege and I can't suggest edits anymore.
Do I have to suggest edits on another Stack Exchange site to get the Miranda hat?
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You can get the hat by suggesting edits on tag wikis until you obtain the Trusted User privilege at 20,000 rep.
Trusted users are allowed to perform trusted actions, including:
[ ... ]
• Editing tag wikis without needing approval
You won't be able to obtain the hat if you have >20,000 rep on a particular site. You can always try to earn that hat on another site where you're able to suggest edits.