jQuery UI 1.12.x has changed the folder structure and files that make up the library compared to version 1.10.4. If you have direct references to any of the old file filenames then you will need to update them to the new name. For example if you previously referenced the tabs widget with "/i/libraries/jquery-ui/1.12.1/ui/minified/jquery.ui.tabs.min.js" it would need to change to "/i/libraries/jquery-ui/1.12.1/ui/widgets/minified/tabs.min.js"
The APEX specific bundle jquery-ui-apex[.min].js that is loaded by default for APEX desktop UI pages (either as jquery-ui-apex.js or as part of desktop[_all].min.js) includes all the core files, the drop effect, and these widgets:
This is essentially the same set as in 1.10.4 with the addition of sortable. If you had a separate reference to sortable it can be removed.
The jquery-ui-apex[.min].css file is loaded by default and includes all the jQuery UI CSS files. If you had references to individual jQuery UI css files they can be removed.