Does Green Flame Blade and Sweeping Attack combo cause the bonus effect of GFB to hit again?

Question

I was theory crafting and came across the combination of Green-Flame Blade with the Battlemaster Fighter's Sweeping Attack maneuver. I understand that just fine. What I am unclear on is this:

I cast GFB and hit target. Then I activate Sweeping Attack to roll a Superiority Die to hit a second foe for the Dice's damage with the same attack (only if the original attack would hit the second foe's AC).

Point of contention: I am required to be able to hit second target with same attack then and only then do I do damage to the second target (The attack is the GFB). Then applying the superiority die as damage. This leads me to believe that because it specifies it being the same attack and that attack having an on-hit effect it should play out as the only thing changing for the second target is the initial weapon damage.

Edit: I see a lot of separation of the spell and an attack. Normally this is the case but in this instance with GFB as well as Booming Blade they are the same. They have spell ranges that are susceptible to spell alterations such as meta magics and feats like Spell Sniper as well.

I end up with one melee weapon attack that hits two different foes with two special effects added to the attack. Is this correct?

Weapon damage + GFB damage. GFB Jump damage to second target. Superiority Dice damage + GFB damage (because it is still the same attack correct?). GFB Jump damage to another target (possibly the original) ((because it states that this happens on a hit with an attack?)).

Answer 1

No, GFB only triggers once

Greenflame blade description says

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, ...

"On a hit" refers to the attack made as part of casting the spell, and the effect only applies to the spell's target if that attack hits.

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Additionally, Sweeping Attack is not even an attack, regardless of the name of the maneuver.

When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.

It only deals damage to target.

"But it is 'the same attack' ..."

even if we liberally interpret the second 'hit' is an attack AND it hits, the spell only affect the spell's target, not the target(s) hit.

So, no, it will only trigger once.

Answer 2

The bouncing effect of green-flame blade will only trigger once

The green-flame blade spell states (emphasis mine):

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell's range, otherwise the spell fails. On a hit, the target suffers the attack's normal effects, and green fire leaps from the target to a different creature of your choice that you can see within 5 feet of it. The second creature takes fire damage equal to your spellcasting ability modifier. [...]

The spell description constantly refers to a single creature that is the target of your melee attack and some different creature that is within 5 feet of them; thus, the spell has only one initial target. The Sweeping Attack Maneuver does not state anywhere that it increases the number of targets of a spell, only the attack itself. Green-flame blade will still only have one initial target so the bouncing effect only triggers once.

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Similarly, the extra damage on the attack will only apply to the first target

The green-flame blade spell goes on to states (emphasis mine):

[...] At 5th level, the melee attack deals an extra 1d8 fire damage to the target [...]

Because there is only that same one target, and Sweeping Attack does not add additional targets for the spell, the second creature would not even take the fire damage that the first one did.

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The Sweeping Attack Maneuver is weird

This feature states (emphasis mine):

When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.

Reading this strictly we can conclude the following:

1. The Maneuver attempts to damage another creature using the same attack; it neither attempts to hit another creature nor does it involve a second attack of any sort.

2. You only damage the second creature if the original attack roll would hit them, not if it actually does hit them.

This feature is, at least to me, rather strange with all this wording. It makes for some weird instances where the second target has no effects on (dis)advantage or where critical hits only affect the first target, but that's how it is worded.

At my own tables I would quite likely rule the second target as actually having been hit by the attack, though I'd have to think more about the implications of that ruling before I made it.