If the shield is big enough to provide cover, it provides cover. The same goes for standing behind a 8 foot tall barbarian. If it’s in between you and the ranged attacker, and its big enough to cover half of your body, it provides cover. Depending on how tall you are and how tall the shield is, it could be half or three quarter cover. It would provide no other benefit.

No.

By raw any creature or object can give you cover with or without a shield, even if most DM's ignore this. There is even a question about it. Do other creatures provide cover?

However an unseen servant is not a creature nor object, it is simply a from-less force as confirmed by J. Crawford So it would not be able to provide cover by itself. So the question becomes, what could a floating shield provide just by itself.

Consider an animated shield which is a magic item that is a better version of the same trick, and just gives you a +2 to AC.

While holding this shield, you can speak its command word as a bonus action to cause it to animate. The shield leaps into the air and hovers in your space to protect you as if you were wielding it, leaving your hands free. The shield remains animated for 1 minute, until you use a bonus action to end this effect, or until you are incapacitated or die, at which point the shield falls to the ground or into your hand if you have one free."

As a DM I would give you +1 to your AC, its clever and you should reward cleverness, but it should not be as good as wielding the shield yourself or using an animated shield, because there will be a significant delay in controlling it. If you are generous DM, say it is the same as an animated shield and give a +2 to AC. Cover has other benefits besides increasing AC, and there is no reason to give a poor duplication of an existing item more benefits than said item.

Unseen servants can certainly hold objects (it is explicitly stated that the servant can interact with objects, and "fetching things" is given as an example of what the servant can do), and large objects certainly create cover. With strength 2, the servant can carry 30lb, or drag 60lb. That should be enough to carry a large enough object to obscure enough of a character to create cover.

There is no guide to how big shields are in D&D, so it is up to your DM to decide if it covers enough to give cover.

Keep in mind an enemy could directly attack the servant, although they would likely have disadvantage on the attack, they would probably kill the servant in 1 hit.

It's up to the DM

Determining if the Servant can do it and what cover it may provide is entirely up to the DM since there are no specific rules about this.

There is a lot for a DM to consider here. Everything from whether or not the Unseen servant has the capability to act like an animated shield (DMG 151) and be able to respond appropriately to how much cover it would actually provide.

Figuring out what works at your table will be a discussion, but it is ultimately the DM's call.

Players narrate, DM turns it into mechanics.

In this use case, the player would announce their intent to have the unseen servant stand in front of them with something big and describe the object being used.

It is then up to the DM to determine if the action will succeed as planned and what type of benefit of cover it provide (PHB, Chapter 9) with my emphasis:

The DM determines whether the target has cover and whether you have advantage or disadvantage against the target.

Success can be on any scale and can involve ability check rolls to see how well the servant does it's job to just agreeing and providing the maximum cover they can think of.