No advantage on the attacks unless already unseen or hidden
I'll get to specific cases in the second part, but if the Ranger begins their turn visible to their enemies, they do not get advantage on any of the attacks. The Ranger is visible when they take their action and chooses to cast an offensive spell. That does not accrue advantage. When you cast an offensive spell you are making an attack. (The rolls themselves are a part of the spell's magical effect).
When a creature can’t see you, you have advantage on attack rolls against it. If you are hidden—both unseen and unheard—when you make an attack, you give away your location when the attack hits or misses.
The Ranger is instructed by the text to "make a melee spell attack" but it does not, unlike its little cousin Zephyr Strike, explicitly grant advantage in the making of this attack.
Once before the spell ends, you can give yourself advantage on one weapon attack roll on your turn. (Zephyr Strike, XGtE).
Absent that explicit language granting advantage, we cannot conclude that Steel Wind Strike grants advantage on the attack(s) by itself. (FWIW, this tweet from the lead dev indicates concurrence with my rules interpretation, but it's unofficial: it didn't make it into the Sage Advice Compendium (Thank you @Medix2, I should have searched for that once I found no SWS in the SAC).
That said, some applications of Steel Wind Strike will (or should) grant advantage on all of the attacks per Cases 2, 3, and 4.
Case 1: Ranger in a room, begins the round visible to enemies
The Ranger uses an action to cast an offensive spell, steel wind trike, and applies the appropriate material and somatic components. (Note for later: no verbal component). At the time the Ranger casts the offensive spell, they are visible. The magical effect of the spell makes a whole host of things happen. Let's examine what is going on with all of these magical effects of this spell that are not the attack rolls?
In casting a spell, a character carefully plucks at the invisible strands of raw magic suffusing the world, pins them in place in a particular pattern, sets them vibrating in a specific way, and then releases them to unleash the desired effect—in most cases, all in the span of seconds. (Basic Rules, p. 82)
What is the significance of the Ranger vanishing to be replaced by something magical that allows them, in the span of seconds, to strike like the wind? How does the wind strike? That's a good question, but if the wind blows through the room or area in which we are standing, we will all feel its effects. Or, you could interpret it as @smbailey did (thank you for the comment)and infer that 'like the wind' means 'really fast' per the idiomatic phrase "run like the wind."
As I consulted various wind spells of fifth level and below I discovered that most of them don't do damage, although investiture of the wind (6th level) can do bludgeoning damage. The consistent theme that I found was that wind (from spells) is air that moves. Gust of wind offers 20 mph, for example. It is this movement - like the wind - that gives the Ranger the ability (speed) to, in one turn, strike multiple targets that are up to 60 feet apart. (I'll drop a picture in later).
Imagine the Ranger in a circular room that is 55 feet in diameter with five hostile ogres equally spaced around its circumference. The Ranger starts in the middle. The ogres are all about 25' from the Ranger and within the spell's range. Normally, the Ranger can't get from one target to the other and attack all five (if they somehow have five attacks for that turn) in one turn - there is not enough movement available. Steel wind strike, through its magical effect, lets the Ranger reach all five of the ogres at once (I'll explain that in a bit).
Again, the offensive spell being cast takes one action, and it leads to from one to five attacks on separate targets happening on the Ranger's turn. That's a big change to how many targets can be attacked, thanks to the spell's magical effect.
The other big change is that the weapon used inflicts, not its usual damage (piercing, bludgeoning, slashing), but instead 6d10 force damage on a hit. This is unique to this spell - the other wind spells I consulted that do damage do bludgeoning damage. Force damage is described as a damage type that is pure magic in nature.
Force. Force is pure magical energy focused into a damaging form. Most effects that deal force damage are spells, including magic missile and spiritual weapon. (Basic Rules p. 78)
And lastly, once all of those attacks go off, the Ranger ends up next to any one of the targets. That's the Teleport function accounted for: the Ranger ends up somwhere else than when they started, somewhat like how misty step works, or dimension door.
Why simultaneous attacks/damage? What leads me to not read this as the Ranger teleporting in sequence from target to target to make sequential melee attacks but rather make the attacks happen all at once, is (1) the spell creating magical effects that let the ranger reach them all at once (strike like the wind) and (2) the spell doing force - pure magic, the weapon is also changed along with the Ranger - damage and (3) we don't see the Ranger reappearing after it hits or misses the last target. We see the Ranger reappear (no longer 'like the wind') next to one of the targets. If the attack had gone in a particular sequence, then the Ranger would be expected to end up next to the last target hit or missed. (I'll find a similar example later, RL calls).
Since the body of a Ranger is a creature it can't be five places at once (per the ogre example above. There isn't enough movement. It is, via the magical effect of the spell, replaced by something 'like the wind' so that it can attack them all 'like the wind' and then, once the attacks are completed, reappear in standard Ranger form. This all takes place in a few seconds.
Case 2: Gloomstalker in an unlit/dark room. Attacks have advantage.
This case grants advantage on all of the attacks thanks to the unique feature of the gloomstalker's sight in places that are dark. The gloomstalker is unseen by all of its intended targets, unless a specific creature can see the gloomstalker via means other than darkvision.
Case 3: Any Ranger begins the round invisible. Attacks have advantage.
This case grants advantage on all of the attacks. The Ranger is both unseen and unheard since there is no verbal component to the spell. (I am pretty sure that this was intentional). The DM may call for a Stealth check to make sure no unintended noise occurs, but being unseen ought to cover this case by itself. The Ranger, upon casting the offensive spell, is unseen unless a specific creature can see them via some kind of 'detect invisible' ability or spell.
Case 4: Any Ranger begins the round hidden. Attacks have advantage.
If the Ranger has already used a class feature to become hidden - such as the 14th level Vanish ability, or the 10th level Hide in Plain Sight ability - the Ranger is unseen and unheard. The unheard is crucial to this. The spell has no verbal component. They'll be visible at the end of the attacks, next to one of the bleeding victims, but advantage accrues to all of the attacks since they all go off at once. It is not until the attack hits, or misses, that the Ranger is revealed to those who survive.
When a creature can’t see you, you have advantage on attack rolls
against it. If you are hidden—both unseen and unheard — when you make
an attack, you give away your location when the attack hits or misses.
Notes on timing
I had begun this answer while thinking that once the first of two, three, four or five attacks had happened all of the others would be made while visible in cases 2 through 4 (attacks in sequence) but as I read through the spell and the supporting material, that no longer made sense once "like the wind" got me looking at what wind spells do.
Why must the Ranger vanish? Changing form is necessary to strike like the wind.
You flourish the weapon used in the casting and then vanish to strike like the wind.
As written in that completed sentence, vanish does not exist as a term by itself, but as the precursor to striking like the wind. Without changing into something else, the Ranger lacks the ability to strike all of those dispersed targets (see ogre example). I challenge the frame of this question; asserting that vanishing provides an additional feature to the spell in a game mechanics sense without explicitly including that feature.
Once the striking "like the wind" is done the Ranger returns to mundane form. Becoming like the wind is the significant magical effect that allows all of those targets to be reached in the space of one turn and to hit them with magical, not mundane, damage.
If the granting of advantage, like in Zephyr Strike, had been included in this spell's text then this answer would not have been presented and I'd not have realized that this spell's features have some unique nuances. So thanks for asking in the first place.
Note: while I used Ranger for this case, as it is a Ranger spell, Wizards and Bards (via Magical Secrets) can also use this spell.