Look at the "attachments" section in your screen shot. It gives three rules - who can create attachments, who can delete their own attachments, and who can delete any attachment.
Your account obviously matches the rule for "delete own", as that says "any logged in user", but the rule for any attachment is "people in a role". Are you in that role in the project?
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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