When I go to Save As → non of the drop down file format options include xlsx. See attached screenshot.
I don’t understand what your problem is. If you specify Excel 2007-365 you will get a .xlsx file.
Does it bother you that file extensions are not visible on the list? This is not the LibreOffice settings, this is the setting of your Windows, one checkbox (usually the third from the bottom) in the section View folder properties, something like “Hide extensions for registered file types” (for example see https://www.youtube.com/watch?v=V9mJ96XBbaw or any other, there are hundreds on YouTube)
@JohnSUN, just for clarification: The Windows setting “hide extensions for known file types” hides them from the drop down list as well? This seems like a non-obvious design choice - since they are serving a different purpose in the drop down than they do in a file manager.
@NisJ It also seemed ridiculous to me. But before writing my comment, I just checked - it really is.
… and that’s the question that Windows “design-choosers” to be asked 
If you specify Excel 2007-365 you will get a .xlsx file. As you can see, the type column starts with Microsoft. They can’t show you the Excel logo, that’s all. If you send it to someone, they will think it is a spreadsheet created in Excel.