There are several file tabs related options in submenu File tabs in context menu of a file tab opened by clicking with secondary (right) button on a file tab.

The file tabs appearance can be even more customized by opening Advanced - Settings or Configuration - Application layout - File tabs.

There is for example at Operation the option Close tab button which can be configured to None to remove symbol × from each file tab which reduces the width of each file tab. A file can be nevertheless closed easily using a pointing device by double clicking with primary (left) or with middle button on a file tab depending on the appropriate file tab options at Miscellaneous.

The width of a file tab can be even more reduced by unchecking file tabs option Display status icons at Miscellaneous.

All the file tab settings in configuration are explained in help of UltraEdit which can be opened by clicking on button Help of opened configuration dialog.

See the forum topic Font size for the File Tabs and the List Views for details how to use a different font with thinner characters or a smaller font size to reduce the width of a file tab depending on used version of UltraEdit.

It looks like "takes up less horizontal space" means something different in Ohio than "how to use more vertical space to get more file tabs displayed at once on long file names in Austria. However, you use now the configuration you like and that is most important.

BTW: The open file tabs bar could be docked also on left or ride side instead of top with using multiline tabs to get the file tabs listed vertically. But in this case I would suggest to use the File View docked on left or right side of main application window with tab Open selected and hide the open file tabs bar completely to get more vertical space for the opened files. See also forum topic What's this dropdown on the 'open files pane'? how handy this view can be used using just keyboard on having many files opened.