How to hide the New text?

The nearest to that I know of is hiding the System text using Vive tool
List of VIVE Tool functions
If you're lucky they may have added a way to deal with 'New'.

My experience of Vivetool is, however, that it is highly build-dependent and a 'fix' is easily broken as time goes on.

I've not yet seen any other reference to 'New' although I do see an example (in English- I'm wondering why yours is a mixed language UI) on my Start Menu.

Here's an idea:
If you dislike the arbitrary changes MS makes to the Start Menu, why not use a 3rd party start menu?

Open Shell is excellent, far more flexible and configurable, supports full drag 'n drop, easy access to the underlying folders, and properly displays a start menu with shortcuts in nested folders (e.g. categories) - which no Win 10 style start menu does.

Also has a good search box.

And no sign of 'New' or 'System'.

Did I say it's free?

It's showing as new because you have recently installed that program. Just click on that program to open it and the new-text will disappear.

If it's a program, yes, probably.

If it's a folder that's marked New - well I have an example - a folder called 'Utilities' with many programs' folders of shortcuts within that (spread out linearly as Win 10's start menu can't cope) - and scrolling and scrolling.. I can't see anything else marked 'New' to explain why the folder's maked 'New'.

Clicking on the folder doesn't remove the 'New' designation.

This is handled properly by Open Shell - which uses highlighting, not text. Easy.