Can a College of Swords bard use the Slashing Flourish option to apply a Smite spell to all creatures in range?

Question

The description of the Wrathful Smite spell says (PHB, p. 289):

The next time you hit with a melee weapon attack during this spell's duration, your attack deals an extra 1d6 psychic damage. Additionally, if the target is a creature, it must make a Wisdom saving throw or be frightened of you until the spell ends. As an action, the creature can make a Wisdom check against your spell save DC to steel its resolve and end this spell.

The College of Swords bard's Slashing Flourish option says:

You can expend one use of your Bardic Inspiration to cause the weapon to deal extra damage to the target you hit and to any other creature of your choice that you can see within 5 feet of you. The damage equals the number you roll on the Bardic Inspiration die.

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So here is our Bard surrounded by enemies:

With a bonus action, he casts Wrathful Smite and then he attacks the Ogre. His attack hits the Ogre, so he grabs the Bardic Inspiration die to roll for Slashing Flourish; he rolls an 8 on the Bardic Inspiration die, so all creatures take 8 extra weapon damage.

1. Does the sword hit all of them? (I assume yes.)
2. Who gets psychic damage?
3. Who makes Wisdom saving throws?
4. Who is frightened?

Sidenote: The Battle Master fighter subclass has a Sweeping Attack maneuver, but its wording does not support the above interpretation of the rules. So no AE Wrathful Smite for the Battle Master.

Answer 1

The orcs have not been hit by a melee weapon attack

Slashing Flourish:

You can expend one use of your Bardic Inspiration to cause the weapon to deal extra damage to the target you hit and to any other creature of your choice that you can see within 5 feet of you.

All of the creatures¹ of your choice are taking damage, but what is dealing the damage? "The weapon" is dealing the damage. It is dealing damage to both "the target you hit" and to other creatures (that you did not hit).

Wrathful Smite:

The next time you hit with a melee weapon attack during this spell's duration, your attack deals an extra 1d6 psychic damage.

Who takes damage from the smite? The target you "hit with the melee weapon attack". What is dealing this damage? "Your attack". The ogre has been hit by a melee weapon attack, but you have not hit the orcs with a melee weapon attack. They have been damaged by your weapon through your slashing flourish, but they were never targets of an attack, and were not hit by the attack, because you did not make attack rolls against them.

Making an attack:

If there's ever any question whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack.

Despite this "simple rule", there are instances in which you are making an attack without making an attack roll; grappling and shoving, for example. The consensus, on this site at least, is that something is an attack only if it includes an attack roll or if its text clearly indicates that it is an attack. Slashing flourish does neither; it is a source of damage but is not, in itself, an attack.

Does the sword hit all of them?
No, the sword damages all of them, but it hits only the ogre.

Who gets psychic damage?
Only the ogre.

Who makes Wisdom Saving rolls?
Only the ogre.

Who is frightened?
Only the ogre, and only if it fails to save.

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¹ _{Note that the ability says "any other creature" of your choice - not "all other creatures of your choice" or "each other creature of your choice". Nonetheless, the intent seems to be that it can, in fact, be applied to multiple creatures.}

Answer 2

Let's analyze each of your question.

1) Does the sword hit all of them?

Yes, since Slashing Fury

cause[s] the weapon to deal extra damage to the target you hit and to any other creature of your choice that you can see within 5 feet of you.

Your sword deals 8 slashing damage in addition to your original damage roll to any enemy you can see and that you choose within 5 feet, per description of the ability.

2) Who gets psychic damage?

Only the ogre gets the psychic damage: indeed, the spell's description says

[...] your attack deals an extra 1d6 psychic damage.

and not your weapon deals an extra 1d6 psychic damage: compare it with the text of Slashing Fury. Then, the psychic damage is added only to the original attack.

3) Who makes Wisdom Saving rolls?

Since the spell is related to the attack, the WIS saving throws are done only by the Ogre: see the above explanation.

4) Who is frightened?

Only the Ogre, per answers to questions 2&3.