How do I remove the "Productivity" group header from Windows 10's Start menu?

How do I remove the “Productivity” group header from Windows 10's Start menu?

All you have to do is click on the words "Productivity" and clear the text.

how can I get rid of the redundant group header and free up the space it's taking up?

You can get rid of the words, but you will be unable to get rid of the unnamed group, if you want that gone you will have to use a Start Menu replacement program.

You can clear the header name, but it doesn't remove the header itself, as it's still there when hovered over and the space it takes up remains there.

Based on your last description, want isn't possible without a third-party program, the best you can do with native functionality is remove the group name. This might change once Windows 10 version 2004 is released.