I’ll assume you’re asking for Linux; I have tried several ways of blurring the background of Firefox window components with page content in the back without success. It seems they’re rendered in entirely separate contexts, as blur effects don’t apply; nor does any other filter that would combine window and page content.

My use case was to blur the background of collapsible vertical tabs when expanded, and blur the bg of the URL bar dropdown. Changing background opacity works, however.