I tried for years to do something there. But when the plugin asks Windows about what is on the window, the OS would say: zero controls. Yes, the normal Windows API doesn't see the controls since they are all done in C++ classes drawing directly into the window. Without a handle to work on, we gave up several attempts to do something.
But a few days ago I looked again on various windows and I noticed that the third tab actually uses a real Win32 control to show the graph for relationships. Probably because this part is older from FileMaker 7 times and didn't get updated with all the controls around. When you click on the relationships tab, FileMaker shows a control there, that the plugin can see.
Now when we have a target to send the search string, we need a field. But we can't see the other controls, so we just place a search field right of the tabs with enough space for all languages. Since we have to watch the current window in FileMaker regularly, it shows up a bit delayed and we remove it when you click to other windows. Please try it in 12.5 pre-release plugin (and update to final one next week).
For the 12.5 release next week, we try to fix all bugs. But for the future we have a few ideas to enhance this. e.g. we may do a popup like on macOS, try to define a shortcut to continue search or try to get it working with asian characters. If you find an issue, please let us know.
Known problems: Seems like you cannot use underscore or point in the search text.