While it's easy to see the RAI written into this item, as per RAW it is utterly broken and mechanically confusing. I suggest the following re-wording to correct it into be written as per RAI. Yes, more text but also more accurate text.

Pearl of Power
Wondrous Item, uncommon (requires attunement by a spellcaster)
While this slightly shimmering pearl is on your person, you can use one action to speak its command word and regain one expended spell slot up to 3rd level. If the expended slot is of 4th level or higher the regained slot counts as only 3rd level in regards to spellcasting until expended or a long rest. A Warlock able to cast level 4 spells will when casting from this regained spellslot cast it at spellevel 3 instead of max spellevel. Once you have used the pearl, it cannot be used again until the next dawn.

I see what you're saying and I think you've misinterpreted. It restores any spell level up to level 4. 

 Quote from Arcavato >>

I see what you're saying and I think you've misinterpreted. It restores any spell level up to level 4. 

I don’t read it that way. It says nothing about regaining spells, but instead expended spell slots.

So if it is the start of a new day and you have all your spells, it is useless. However if you cast a 4th level spell, and no other spells, and use it you get a 3rd level slot back instead of a 4th level slot. You would be unable to cast the same 4th level spell again using the item, but would instead get a new 3rd level(or 1st or 2nd) to use instead.

the confusion only really applies to warlocks who can only cast spells at their max level.

No they only have slots normally at their max level. A warlock with a pearl of power would at best get a 3rd level slot.

So... Artificers can not make these right via Infusion replicate magic.  its not on the class list, and its not featured in xanathars right? so its invalid choice?

That's correct. Though PCs can create magical items during downtime by spending gold and time. 

If this item requires attunement by a Spellcaster, why is it not set up to take an attunement slot? 

Quote from PikeWolfgard >>

If this item requires attunement by a Spellcaster, why is it not set up to take an attunement slot? 

That appears to be working now.

Per RAW, this item doesn’t seem to work with warlocks, as it requires attunement by a Spellcaster (which refers to the Spellcasting class feature as it's capitalized) and warlocks have the Pact Magic feature, which is technically different. This would clear up confusion related to warlocks.

No attunement by spellcaster means "Attunement (p. 136). The first paragraph ends with a new sentence: “If the prerequisite is to be a spellcaster, a creature qualifies if it can cast at least one spell using its traits or features, not using a magic item or the like."" (This is from a DMG errata). So Warlocks should be able to use this.

I hadn’t read sage advice, you are correct

What does a cursed version of this item do?

Regain a 3rd level spell slot but take HP or regain a 3rd level slot but takes a 1st level slot

What class of magic does this belong to?

All caster classes can use it.

Quote from LauraSells01 >>

What does a cursed version of this item do?

 There’s no official version, of course, but I imagine it might bring some sort of spell slot fatigue. 

Quote from LauraSells01 >>

What does a cursed version of this item do?

 I've seen a similar item in a third party module that causes one hit die worth of necrotic damage every time you use it. 

There is a Cursed one in the Rime of the frost maiden module, while carrying it you are prevented from gaining the benefits of a long rest

Basically you need to have expended at least one spell slot before using this item's ability with a command word, when you do, you gain an extra, temporary 3rd spell slot (or lower, but you could just cast a 1st or 2nd at the level of a 3rd if you wanted) - can't be used again until the next dawn

TLDR - This item is a temporary, extra 3rd spell slot (or lower) that recharges each day

This item is so useful for warlocks. If you have a 7th level warlock, this pearl, and a rod of the pact keeper, you can basically gain a 3rd and 4th level spell slot after expending your original slots. It's a lifesaver if short rests are scarce.