Spirit Shroud Says:

any attack you make deals 1d8 extra damage when you hit a creature within 10 feet of you.

Green-flame blade Says:

On a hit, the target suffers the weapon attack’s normal effects, and you can cause green fire to leap from the target to a different creature of your choice that you can see within 5 feet of it.

To me that sounds like the single attack is damaging 2 creatures, and spirit shroud should apply to both.

Does the target of the secondary damage of Green-flame blade also receive the Spirit Shroud damage?

The description of the spirit shroud spell says (emphasis mine):

any attack you make deals 1d8 extra damage when you hit a creature within 10 feet of you.

The description of the green-flame blade spell says (emphasis mine):

On a hit, the target suffers the weapon attack’s normal effects, and you can cause green fire to leap from the target to a different creature of your choice that you can see within 5 feet of it.

To me, that sounds like the single attack from green-flame blade is damaging 2 creatures, and the extra damage from spirit shroud should apply to both creatures.

Does the target of the secondary damage of green-flame blade also receive the extra damage from spirit shroud?