I had begun this question with frustration, but then accidentally stumbled upon the solution. :)
If you wish to search for URL inside Confluence content, use the following regex expression syntax:
/.*{URL}.*/
For example, I wanted to find every Confluence reference to our deprecated Google Site, so I searched for: /.*sites.google.com.*/
JOY!
Update:
Davin Studer goes into more detail on how to make regular expression queries in Confluence. Thanks @Davin Studer!
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