How can I hide taskbar labels in Windows 10 without combining icons?

7+ Taskbar Tweaker can do that. Just check Don't combine grouped buttons in Combining section.

In order to do this, simply set your taskbar setting to "Always combine, hide labels". Then, download 7+ Taskbar Tweaker and under "Combining" choose "Don't combine grouped buttons".

You will effectively get: "Never combine, hide labels". Hope this helps.