How do ball bearings and difficult terrain stack?

There is already this Q/A on whether difficult terrains stack (they do not). And this Q/A on whether ball bearings and caltrops stack (they do not). But when looking at the description for ball bearings I realized it states:

A creature moving through the area at half speed doesn’t need to make the saving throw…

And when looking for other references to “half speed” all that existed were caltrops (with a similar description) and this bit from the “Difficult Terrain” section:

You move at half speed in difficult terrain–moving 1 foot in difficult terrain costs 2 feet of speed–so you can cover only half the normal distance in a minute, an hour, or a day…

I had always assumed you could choose to move at half speed through ball bearings to avoid the saving throw but perhaps that is not the case…

Regardless, it is unclear to me what happens if ball bearings are thrown onto difficult terrain. You would (outside of features such as the Ranger’s Land’s Stride) already be moving at half speed due to the difficult terrain but do ball bearings require it to be halved again, or is putting ball bearings on difficult terrain useless unless a creature that ignores difficult terrain?