Ok, I’ll report back, in the hope that this post may help someone in the future.
First, seeing the posts / question answered about other popup windows was helpful. In particular when it was mentioned that the window url should be included in the UI element target; being that my popup had a different url, this part was important.
Once I added that, the RPA was able to type the code into the search field and click the search button (the popup window was now correctly in front of the main application browser window.)
My second problem was when the search was complete, a table was made visible with the (singular) result from the product search.
I wanted to grab the text from the 1st cell to compare the model numbers to be sure they matched.
Even with the url, along with other tuning of the UI selector for that field, the GetText activity was NOT pulling the value out of the cell.
I then remembered this was a table that I was working with and switched to the Extract Table Data activity which successfully pulled out the value that I needed so the RPA could continue validating the results.
At that point the RPA was finished with the popup window and closed it.
Hopefully these tips may help someone in the future.
-Will