dnd 5th – Does Flaming Sphere do fire and / or radiation damage?

No

The spell specifies the damage in the last sentence of the first paragraph.

The creature takes 2d6 Fire damage in case of failure of a save, or half of its damage if successful.

So moving the sphere into a creature and forcing a saving throw against the damage just causes fire damage.

If you push the sphere into a creature, that creature
must make the saving throw against the
damage, and the sphere stops moving this turn.

It only states explicitly that it emits light or ignites objects;

The sphere ignites flammable objects that are neither worn nor worn. It emits bright light in a 20-foot radius and dim light for another 20 feet.

If it was to cause radiant damage, it would be explicitly stated.