Answered
"An extra border appeared outside the object itself."
"This just happened: right after I applied Effect → Blur → Gaussian Blur to a circular object, a bounding box appeared around it. How can I get rid of this outer box?"

"This just happened: right after I applied Effect → Blur → Gaussian Blur to a circular object, a bounding box appeared around it. How can I get rid of this outer box?"

You may want to deselect and select the object after changing the option to see the change.
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