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Harry has the invisibility cloak, one of the three most powerful objects in the wizarding world.

With time, more and more people learn the fact that Harry has it, however, nobody really cares. Shouldn't that be a big deal?

The Death Eaters went so far for the Elder Wand, did none of them know that Harry also possessed a Deathly Hallow?

The Death Eaters didn't go after the Elder Wand, Voldemort did. There is a distinction - Voldemort never told anyone that he was looking for the wand, even Snape, who he believed was his most loyal supporter.

Nobody really knew about the Hallows, and the credibility of their existence is brought into more doubt by Xenophilius Lovegood believing in them - as Ron says, they were regarded by most wizards as a fable in order to make people behave themselves.

In Chapter Twenty-Two of Deathly Hallows we see Harry thinking about Voldemort going after the Hallows:

Voldemort had been raised in a Muggle orphanage. Nobody could have told him The Tales of Beedle the Bard when he was a child, any more than Harry had heard them. Hardly any wizards believed in the Deathly Hallows. Was it likely that Voldemort knew about them?

Harry gazed into the darkness.... If Voldemort had known about the Deathly Hallows, surely he would have sought them, done anything to possess them: three objects that made the possessor master of Death? If he had known about the Deathly Hallows, he might not have needed Horcruxes in the first place. Didn’t the simple fact that he had taken a Hallow, and turned it into a Horcrux, demonstrate that he did not know this last great Wizarding secret?

Which meant that Voldemort sought the Elder Wand without realizing its full power, without understanding that it was one of three... for the wand was the Hallow that could not be hidden, whose existence was best known... The bloody trail of the Elder Wand is splattered across the pages of Wizarding history...

So it seems that Voldemort was unaware of the Hallows. This is confirmed by Dumbledore in Chapter Thirty-Five of Deathly Hallows:

“And Voldemort never knew about the Hallows?”

“I do not think so, because he did not recognize the Resurrection Stone he turned into a Horcrux. But even if he had known about them, Harry. I doubt that he would have been interested in any except the first. He would not think that he needed the Cloak, and as for the stone, whom would he want to bring back from the dead? He fears the dead. He does not love.”

This latter quote also tells us that even knowing about the Hallows wouldn't necessarily make someone interested in them, since aside from the Elder Wand they aren't necessarily so useful.

While the above quotes speak about Voldemort, we have no reason to assume that the Death Eaters were more aware of the Hallows than Voldemort. In fact, contrary to the assertion in the question here, it was Voldemort and not the Death Eaters who went after the Elder Wand.

Additionally, Harry's possession of the Invisibility Cloak was not such public knowledge. In Deathly Hallows the Death Eaters knew that he had the Cloak:

"Accio Cloak!" roared one of the Death Eaters.

Harry seized his folds, but it made no attempt to escape. The Summoning Charm had not worked on it. "Not under your wrapper, then, Potter?" yelled the Death Eater who had tried the charm and then to his fellows.

"Someone's there," came a rough whisper close at hand. "He's got an Invisibility Cloak. Could it be –?"

Yet as late as Chapter Six of Half-Blood Prince Harry was not sure if the Ministry knew that he had a Cloak:

He had stowed his Invisibility Cloak in his backpack and felt that, if that was good enough for Dumbledore, it ought to be good enough for the Ministry, though now he came to think of it, he was not sure the Ministry knew about his cloak.

Additionally, even if the Death Eaters knew about the Hallows, and knew that Harry had the Invisibility Cloak, they still wouldn't necessarily know that it was the Invisibility Cloak. After all, as explained by Xenophilius Lovegood in Chapter Twenty-One of Deathly Hallows, there are other Invisibility Claoks besides the one that it is a Hallow:

"Mr. Lovegood," Hermione began again, "We all know that there are such things as Invisibility Cloaks. They are rare, but they exist. But –"

"Ah, but the Third Hallow is a true Cloak of Invisibility, Miss Granger! I mean to say, it is not a traveling cloak imbued with a Disillusionment Charm, or carrying a Bedazzling Hex, or else woven from Demiguise hair, which will hide one initially but fade with the years until it turns opaque. We are talking about a cloak that really and truly renders the wearer completely invisible, and endures eternally, giving constant and impenetrable concealment, no matter what spells are cast at it. How many cloaks have you ever seen like that, Miss Granger?"

So in short, to address all your points:

• The Death Eaters didn't go after the Elder Wand


• The Cloak was not really that powerful (or at least not perceived as powerful)


• The Hallows were not well known


• Harry's possession of the Cloak only became known pretty late


• The uniqueness of Harry's Cloak was not known

The true age of the cloak was not public knowledge. Neither was its resistance to spells.

Without knowing either of those facts, it might as well be any other invisibility cloak. They’re rare, but we hear of several others during the course of the books, such as the one Barty Crouch Jr. said he was hidden under in book 4.

In addition, “very, very few wizards believe” in the Deathly Hallows, as Xenophilius says in book 7.

For Death Eaters, the far better prize was Harry himself, since Voldemort was interested in him (not his invisibility cloak).