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I don't think the UI quick action will work as you are not actually on a record but a popup as you mention. Have you tried a URL link instead, it will open a new window but might pop the record for you.
With OpenRecord Option - Search with RecID
This works using a URL button on the popup screen with this URL:
you can replace the server name with the $(ServerURL()) syntax if you want may take a little fiddling to get right.
This can be done for any popup object, change, problem etc. Just change the url to suit.