Selecting only visible lines which would be of course multiple selections in file and then copying the displayed lines is not possible in UE v21.00 and all previous versions of UltraEdit as well as in UES v14.10 and all previous versions of UEStudio.
But you can use
Edit - Delete - Delete All Hidden Lines and use next
File - Save As if you want the visible lines saved into a new file.
Or if file is saved before running the Find resulting in hiding lines, you can use after the find the command
Edit - Delete - Delete All Hidden Lines, then press Ctrl+A and Ctrl+C to copy the remaining lines and use now
File - Revert to Saved to restore the original contents of the file.
Of course both methods work only for a file opened with the usage of a temporary file.
For very large files opened without usage of a temporary file and therefore the command
Edit - Delete - Delete All Hidden Lines makes the changes on original file without the possibility to undo it, it is necessary first to make a copy of the entire file and then perform the Find and the deletion of all hidden lines.
Finally, with a regular expression replace it is possible to delete the lines of no interest directly.
Or the find option
List Lines Containing String is used to list all lines of interest in a modeless dialog window or a view (depends on version of UltraEdit/UEStudio) and next the command (button or context menu item) for copying the list of found lines to clipboard is used. It would be also possible to use Find in Files to get all lines of interest into a new file.
And last but not least, one of the scripts available at
Find strings with a regular expression and output them to new file can be used to find data or entire lines of interest and get them copied into a new file.