Only one of the methods listed on the Adobe Illustrator help page regarding adding gradient swatches actually works..

There is no 'Add to Swatches' button in the Gradient menu (in fact, there is no Gradient menu, only a Gradient panel).

Dragging the Gradient fill box from the Gradient Panel to the Swatches panel does absolutely nothing.

Furthermore, the instructions 'Click the swatches menu in the Swatches panel and choose New Swatch' fails to explain the fact that you need to have your gradient selected and active in the active Fill or Stroke boxes.

On top of all of this, all of these functions mentioned above work differently in InDesign and Photoshop. InDesign has an 'Add Gradient Swatch' button in the swatches panel. Since the Gradient panel has been updated in Photoshop, it now has 'Gradient Presets'.

Still no consistency in Adobe software in 2020.