RAW: you don’t get any condition that grants advantage on attack rolls.

The description of the Steel Wind Strike spell says (XGtE, p. 166; emphasis mine):

You flourish the weapon used in the casting and then vanish to strike like the wind. Choose up to five creatures you can see within range. Make a melee spell attack against each target. On a hit, a target takes 6d10 force damage.

You can then teleport to an unoccupied space you can see within 5 feet of one of the targets you hit or missed.

The description says that you “vanish”, not that you gain the invisible condition, nor that you are unseen in any term of game mechanics. The description of the spell would have specified such condition, as it happens for other spells or class abilities (some examples are down below). After having resolved all the attacks, you can teleport next to one target. Note that the description does not says You reappear and you can then teleport […]: if the description assumed the meaning of “becoming unseen” for “vanishing”, then there would be some indication of what happens after the spell ends. Moreover, in this way (vanishing=become unseen) there are no indications when some enemies have truesight or similar ability.

Hence, this spell allows you to attack simultaneously up to five enemies and then teleport next to one of your targets: during each attack you are not invisible or under some condition that grants you advantage on attack rolls.

Recall that spells only do what they say they do. For example, the Shadow Blade (XGtE, p. 164) spell says

In addition, when you use the sword to attack a target that is in dim light or darkness, you make the attack roll with advantage.

Here it is explicitly said that you roll with advantage (under certain environment conditions). Another example is Zephyr Strike (XGtE):

Once before the spell ends, you can give yourself advantage on one weapon attack roll on your turn. That attack deals an extra 1d8 force damage on a hit. Whether you hit or miss, your walking speed increases by 30 feet until the end of that turn.

Spells that grant one or more conditions which may give advantage on rolls explicitly stress out such conditions (as per Invisibility spell, Basic Rules , pg. 254). Other spell, on the other hand, have a more general description, but searching in the PHB you can find the correct interpretation. For example, Darkness produces…well, darkness, and you can find the consequences of this spell here:

A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature effectively suffers from the blinded condition when trying to see something in that area..

Furthermore, there are some uses in the PHB of the verb vanish and when its equivalence in game terms is required the text is pretty clear:

Banishing Smite spell:

[…] If the target is native to the plane you’re on, the creature vanishes into a harmless demiplane. While there, the target is incapacitated.

Blink spell:

On a roll of 11 or higher, you vanish from your current plane of existence and appear in the Ethereal Plane (the spell fails and the casting is wasted if you were already on that plane)

Channel Divinity, Cloak of Shadow:

Starting at 6th level, you can use your Channel Divinity to vanish. As an action, you become invisible until the end of your next turn. You become visible if you attack or cast a spell.

Vanish (ranger):

Starting at 14th level, you can use the Hide action as a bonus action on your turn. Also, you can’t be tracked by nonmagical means, unless you choose to leave a trail.

Misty Escape (warlock):

Starting at 6th level. you can vanish in a puff of mist in response to harm. When you take damage, you can use your reaction to turn invisible and teleport up to 60 feet to an unoccupied space you can see. You remain invisible until the start of your next turn or until you attack or cast a spell.