Can’t add or remove widgets from Today View, only move them around

Today I noticed that I can’t edit widgets in Today View on my iPhone. I can move the ones I had there, but there’s no option to remove or add new ones. The widgets that are already present (battery, calendar…) work fine, but I wanted to add some new ones and it seems impossible. Clicking and holding the screen does nothing (and yes, I did it with my iPhone unlocked acceding from the Home Screen). This issue is only present in Today View (home works as expected).